X-Git-Url: https://git.lyx.org/gitweb/?a=blobdiff_plain;f=lib%2Fexamples%2Fbeamerlyxexample1.lyx;h=922cee1048d4b2c31b9eb95db34ecd32d451f7c6;hb=6012beb90eb88011d1213c9ae38c4a77d711737e;hp=18c194f8422e17d0a49e7506c50fbabecea8e0b0;hpb=9f4cc3c9f07b3e3f67894bd21b3d605131f62025;p=lyx.git

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 18c194f842..922cee1048 100644
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,7 +1,9 @@
-#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 245
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
 \textclass beamer
 \begin_preamble
 \beamertemplateshadingbackground{red!5}{structure!5}
@@ -26,6 +28,10 @@
 
 \newcommand{\Lang}[1]{\operatorname{\text{\textsc{#1}}}}
 
+% This gets defined by beamerbasecolor.sty, but only at the beginning of
+% the document
+\colorlet{averagebackgroundcolor}{normal text.bg}
+
 \newcommand{\tape}[3]{%
   \color{structure!30!averagebackgroundcolor}
   \pgfmoveto{\pgfxy(-0.5,0)}
@@ -145,35 +151,83 @@
 }
 \end_preamble
 \options notes=show
+\use_default_options false
+\maintain_unincluded_children false
 \language english
+\language_package default
 \inputencoding auto
-\fontscheme times
+\fontencoding global
+\font_roman "lmodern" "default"
+\font_sans "lmss" "default"
+\font_typewriter "lmtt" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
 \graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
 \paperfontsize default
 \spacing single
+\use_hyperref false
 \papersize default
-\use_geometry false
-\use_amsmath 2
+\use_geometry true
+\use_package amsmath 2
+\use_package amssymb 2
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
 \cite_engine basic
+\cite_engine_type default
+\biblio_style plain
 \use_bibtopic false
+\use_indices false
 \paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
 \secnumdepth 2
 \tocdepth 2
 \paragraph_separation indent
-\defskip medskip
-\quotes_language english
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
 \tracking_changes false
-\output_changes true
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
 \end_header
 
 \begin_body
 
 \begin_layout Title
 The Complexity of
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Finding Paths in Tournaments
 \end_layout
 
@@ -182,13 +236,15 @@ Till Tantau
 \end_layout
 
 \begin_layout Institute
-International Computer Schience Institute
-\newline
+International Computer Science Institute
+\begin_inset Newline newline
+\end_inset
+
 Berkeley, California
-\begin_inset OptArg
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 ICSI
 \end_layout
 
@@ -201,12 +257,23 @@ ICSI
 January 30th, 2004
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Outline
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
-\begin_inset LatexCommand \tableofcontents{}
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
 
 \end_inset
 
@@ -214,7 +281,7 @@ Outline
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [pausesections]
 \end_layout
@@ -224,86 +291,55 @@ status collapsed
 
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \begin_inset ERT
-status collapsed
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 % Show the table of contents at the beginning
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 % of every subsection.
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
-AtBeginSubsection[]{
+AtBeginSubsection[]{%
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 frame<handout:0>{ 
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 frametitle{Outline}   
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 tableofcontents[current,currentsubsection] 
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
   }
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -321,10 +357,20 @@ Introduction
 What are Tournaments?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments Consist of Jousts Between Knights
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Columns
 
 \end_layout
@@ -336,101 +382,89 @@ Tournaments Consist of Jousts Between Knights
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{1.25cm}{-1cm}{7cm}{4cm}      
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodebox{A}[virtual]{
 \backslash
-pgfxy(2,1)}{
-\backslash
-pgfuseimage{knight1}}{2pt}{2pt}
+pgfxy(2,1)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight1}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 pgfnodebox{B}[virtual]{
 \backslash
-pgfxy(6,1)}{
-\backslash
-pgfuseimage{knight2}}{2pt}{2pt}
+pgfxy(6,1)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight2}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 pgfnodebox{C}[virtual]{
 \backslash
-pgfxy(4,-1)}{
-\backslash
-pgfuseimage{knight3}}{2pt}{2pt}
+pgfxy(4,-1)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight3}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 pgfnodebox{D}[virtual]{
 \backslash
-pgfxy(4,3)}{
-\backslash
-pgfuseimage{knight4}}{2pt}{2pt}
-\end_layout
-
-\begin_layout Standard
-
+pgfxy(4,3)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight4}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<3->{
 \backslash
@@ -439,99 +473,68 @@ pgfsetendarrow{
 pgfarrowto}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
-only<2->{
-\end_layout
-
-\begin_layout Standard
-
+only<2->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A}{B}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A}{C}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D}{A}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C}{B}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B}{D}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
-pgfnodeconnline{C}{D}}
+pgfnodeconnline{C}{D}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -548,12 +551,11 @@ end{pgfpicture}
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status open
 
-{What is a Tournament?}
+\begin_layout Plain Layout
+What is a Tournament?
 \end_layout
 
 \end_inset
@@ -563,12 +565,12 @@ status inlined
 
 \begin_deeper
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<1->
+1-
 \end_layout
 
 \end_inset
@@ -577,12 +579,12 @@ A group of knights.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<2->
+2-
 \end_layout
 
 \end_inset
@@ -591,12 +593,12 @@ Every pair has a joust.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<3->
+3-
 \end_layout
 
 \end_inset
@@ -606,10 +608,28 @@ In every joust one knight wins.
 
 \end_deeper
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments are Complete Directed Graphs
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Columns
 
 \end_layout
@@ -621,115 +641,75 @@ Tournaments are Complete Directed Graphs
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{1.5cm}{-1cm}{6.5cm}{4cm}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{A}{
 \backslash
 pgfxy(2.5,1)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{B}{
 \backslash
 pgfxy(5.5,1)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{C}{
 \backslash
 pgfxy(4,-0.5)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{D}{
 \backslash
 pgfxy(4,2.5)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{white}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -738,13 +718,9 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$v_2$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -753,13 +729,9 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$v_3$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -768,13 +740,9 @@ pgfnodecenter{C}}{
 pgfbox[center,center]{$v_4$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -783,131 +751,79 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$v_1$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetendarrow{
 \backslash
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodesetsepstart{2pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodesetsepend{4pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{A}{B}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{A}{C}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{D}{A}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{C}{B}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{B}{D} 
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodeconnline{D}{C}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -924,21 +840,25 @@ end{pgfpicture}
 \end_layout
 
 \begin_layout Definition
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<2->
+2-
 \end_layout
 
 \end_inset
 
-A 
+A
+\color none
+ 
 \color red
 tournament
-\color default
- is a
+\color none
+ 
+\color inherit
+is a
 \end_layout
 
 \begin_deeper
@@ -948,33 +868,53 @@ directed graphs,
 
 \begin_layout Enumerate
 with exactly one edge between
-\newline
+\begin_inset Newline newline
+\end_inset
+
 any two different vertices.
 \end_layout
 
 \end_deeper
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 2
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-[<+>]
++
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments Arise Naturally in Different Situations
 \end_layout
 
-\begin_layout ExampleBlock
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
 
-{Applicatins in Ordering Theory}
+\end_layout
+
+\begin_deeper
+\begin_layout ExampleBlock
+\begin_inset Argument 2
+status collapsed
+
+\begin_layout Plain Layout
+Applications in Ordering Theory
 \end_layout
 
 \end_inset
@@ -986,22 +926,26 @@ status inlined
 \begin_layout Standard
 Elements in a set need to be sorted.
  
-\newline
+\begin_inset Newline newline
+\end_inset
+
 The comparison relation may be cyclic, however.
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout ExampleBlock
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Applications in Sociology}
+\begin_layout Plain Layout
+Applications in Sociology
 \end_layout
 
 \end_inset
@@ -1012,24 +956,27 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 Several candidates apply for a position.
-\newline
-Reviewers decide for any two candidates
- whom they prefer.
+\begin_inset Newline newline
+\end_inset
+
+Reviewers decide for any two candidates whom they prefer.
  
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout ExampleBlock
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Applications in Structural Complexity Theory}
+\begin_layout Plain Layout
+Applications in Structural Complexity Theory
 \end_layout
 
 \end_inset
@@ -1048,7 +995,9 @@ A language
 \end_inset
 
 .
-\newline
+\begin_inset Newline newline
+\end_inset
+
 It chooses from any two words the one more likely to be in 
 \begin_inset Formula $f$
 \end_inset
@@ -1056,110 +1005,160 @@ It chooses from any two words the one more likely to be in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection
 What Does ``Finding Paths'' Mean?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 ``Finding Paths'' is Ambiguous
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
-\begin_inset ERT
-status inlined
+\begin_inset Argument 2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
+Input for 
+\begin_inset Flex Only
+status open
 
-{
-\backslash
-strut Input for 
-\backslash
-ignorespaces
-\backslash
-def
-\backslash
-par{}% because LyX inserts superfluous paragraphs
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+1
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
+Path Finding Problems
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<1>{Path Finding Problems}
-\backslash
-ignorespaces
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+2-3
 \end_layout
 
-\begin_layout Standard
+\end_inset
+
+
+\begin_inset Formula $\Lang{reach}$
+\end_inset
+
 
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<2-3>{$
-\backslash
-Lang{reach}$}
-\backslash
-ignorespaces
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+4-5
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
+the Construction Problem
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<4-5>{the Construction Problem}
-\backslash
-ignorespaces
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+6-7
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
+the Optimization Problem
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<6-7>{the Optimization Problem}
-\backslash
-ignorespaces
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+8-9
 \end_layout
 
-\begin_layout Standard
+\end_inset
+
+
+\begin_inset Formula $\Lang{distance}$
+\end_inset
+
 
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<8-9>{$
-\backslash
-Lang{distance}$}
-\backslash
-ignorespaces
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+10-
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
+the Approximation Problem
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-only<10->{the Approximation Problem}}
 \end_layout
 
 \end_inset
@@ -1169,27 +1168,39 @@ only<10->{the Approximation Problem}}
 
 \begin_deeper
 \begin_layout Itemize
-A 
+A
+\color none
+ 
 \color red
 graph
-\color default
+\color none
  
+\color inherit
+
 \begin_inset Formula $G=(V,E)$
 \end_inset
 
-, a 
+, a
+\color none
+ 
 \color red
 source
-\color default
+\color none
  
+\color inherit
+
 \begin_inset Formula $s\in V$
 \end_inset
 
- and a 
+ and a
+\color none
+ 
 \color red
 target
-\color default
+\color none
  
+\color inherit
+
 \begin_inset Formula $t\in V$
 \end_inset
 
@@ -1197,21 +1208,26 @@ target
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<only@-9| visible@8->
+only@-9| visible@8-
 \end_layout
 
 \end_inset
 
-A 
+A
+\color none
+ 
 \color red
 maximum distance
-\color default
-\InsetSpace ~
+\color inherit
+
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $d$
 \end_inset
@@ -1220,7 +1236,7 @@ maximum distance
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1233,21 +1249,25 @@ phantom{p}
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<only@10->
+only@10-
 \end_layout
 
 \end_inset
 
-An 
+An
+\color none
+ 
 \color red
 approximation ratio
-\color default
+\color none
  
+\color inherit
+
 \begin_inset Formula $r>1$
 \end_inset
 
@@ -1259,7 +1279,7 @@ approximation ratio
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1272,19 +1292,12 @@ nointerlineskip
 \end_layout
 
 \begin_layout Overprint
+\begin_inset Argument item:1
+status open
 
-\end_layout
-
-\begin_deeper
-\begin_layout Standard
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
-
+\begin_layout Plain Layout
 
-\backslash
-onslide<1,3,5,7,9,11-12>
+1,3,5,7,9,11-12
 \end_layout
 
 \end_inset
@@ -1292,13 +1305,13 @@ onslide<1,3,5,7,9,11-12>
 
 \end_layout
 
+\begin_deeper
 \begin_layout Columns
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 1
+status open
 
-[t,onlytextwidth]
+\begin_layout Plain Layout
+t,onlytextwidth
 \end_layout
 
 \end_inset
@@ -1308,20 +1321,35 @@ status inlined
 
 \begin_deeper
 \begin_layout Standard
-\begin_inset ERT
-status inlined
+\begin_inset Flex Alternative
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+1-2
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 2
+status open
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
 
 
 \backslash
-alt<1-2>{
-\backslash
-column{
-\backslash
-textwidth}}{
+column{
 \backslash
-column{5cm}}
+textwidth}
 \end_layout
 
 \end_inset
@@ -1329,13 +1357,35 @@ column{5cm}}
 
 \end_layout
 
-\begin_layout ExampleBlock
+\end_inset
+
+
 \begin_inset ERT
-status inlined
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+column{5cm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
 
-\begin_layout Standard
 
-{Example Input}
+\end_layout
+
+\begin_layout ExampleBlock
+\begin_inset Argument 2
+status collapsed
+
+\begin_layout Plain Layout
+Example Input
 \end_layout
 
 \end_inset
@@ -1346,42 +1396,42 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{2.5cm}{-0.6cm}{7.5cm}{2.6cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1390,11 +1440,11 @@ graphnode{A}{
 pgfxy(3,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1403,11 +1453,11 @@ graphnode{B}{
 pgfxy(5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1416,11 +1466,11 @@ graphnode{C}{
 pgfxy(4,0)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1429,30 +1479,30 @@ graphnode{D}{
 pgfxy(4,2)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 color{white}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1463,11 +1513,11 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$t$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1478,30 +1528,30 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$s$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1510,107 +1560,107 @@ pgfsetendarrow{
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodesetsepstart{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodesetsepend{4pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{A}{B}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{A}{C}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{D}{A}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{C}{B}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{B}{D}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfnodeconnline{D}{C}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1623,11 +1673,11 @@ pgfxy(5.3,1)}{
 pgfbox[left,center]{, $d=2$}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1640,11 +1690,11 @@ pgfxy(5.3,1)}{
 pgfbox[left,center]{, $r=1.5$}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1657,11 +1707,11 @@ pgfxy(5.3,1)}{
 pgfbox[left,center]{, $r=1.25$}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1675,16 +1725,34 @@ end{pgfpicture}
 
 \end_deeper
 \begin_layout Standard
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+3-
+\end_layout
+
+\end_inset
+
+
 \begin_inset ERT
-status inlined
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
-only<3->{
-\backslash
-column{5cm}}
+column{5cm}
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -1693,12 +1761,22 @@ column{5cm}}
 \end_layout
 
 \begin_layout ExampleBlock
-\begin_inset ERT
-status inlined
+\begin_inset Argument 1
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
+only@3-
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 2
+status collapsed
 
-<only@3->{Example Output}
+\begin_layout Plain Layout
+Example Output
 \end_layout
 
 \end_inset
@@ -1709,126 +1787,82 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{2.5cm}{-0.6cm}{7.5cm}{2.6cm}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
-only<5-8,10->{
-\end_layout
-
-\begin_layout Standard
-
+only<5-8,10->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{A}{
 \backslash
 pgfxy(3,1)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{B}{
 \backslash
 pgfxy(5,1)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{C}{
 \backslash
 pgfxy(4,0)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{D}{
 \backslash
 pgfxy(4,2)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 color{white}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
@@ -1837,13 +1871,9 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$t$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
@@ -1852,159 +1882,94 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$s$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+color{beamerexample}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfsetendarrow{
+\backslash
+pgfarrowto}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodesetsepstart{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-color{beamerexample}
+pgfnodesetsepend{4pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+alert<7,12>{
+\backslash
+pgfnodeconnline{A}{B}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfsetendarrow{
+alert<5,11>{
 \backslash
-pgfarrowto}
+pgfnodeconnline{A}{C}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+alert<5,7,11-12>{
+\backslash
+pgfnodeconnline{D}{A}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodesetsepstart{2pt}
+alert<5,11>{
+\backslash
+pgfnodeconnline{C}{B}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B}{D}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodesetsepend{4pt}
+pgfnodeconnline{D}{C}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-                      
-\end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-alert<7,12>{
-\backslash
-pgfnodeconnline{A}{B}}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-alert<5,11>{
-\backslash
-pgfnodeconnline{A}{C}}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-alert<5,7,11-12>{
-\backslash
-pgfnodeconnline{D}{A}}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-alert<5,11>{
-\backslash
-pgfnodeconnline{C}{B}}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B}{D}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{D}{C}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  }
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  
 \backslash
 only<3,9>{
 \backslash
@@ -2017,11 +1982,7 @@ pgfbox[left,center]{
 alert{``Yes''}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2035,15 +1996,14 @@ end{pgfpicture}
 
 \end_deeper
 \end_deeper
-\begin_layout Standard
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\end_deeper
+\begin_layout Overprint
+\begin_inset Argument item:1
+status open
 
+\begin_layout Plain Layout
 
-\backslash
-onslide<2,4,6,8,10>
+2,4,6,8,10
 \end_layout
 
 \end_inset
@@ -2051,13 +2011,13 @@ onslide<2,4,6,8,10>
 
 \end_layout
 
+\begin_deeper
 \begin_layout Block
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Variants of Path Finding Problems}
+\begin_layout Plain Layout
+Variants of Path Finding Problems
 \end_layout
 
 \end_inset
@@ -2066,65 +2026,69 @@ status inlined
 \end_layout
 
 \begin_deeper
-\begin_layout Standard
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_layout Description
+\begin_inset Argument item:1
+status open
 
+\begin_layout Plain Layout
 
-\backslash
-usedescriptionitemofwidthas{Approximation Problem:}
+2-
 \end_layout
 
 \end_inset
 
-
-\end_layout
-
-\begin_layout Description
-Reachability\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-<2->
-\end_layout
-
+Reachability
+\begin_inset space ~
 \end_inset
 
-Is there a path from 
+Problem: Is there a path from 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
 
 ?
+\begin_inset Argument 2
+status open
+
+\begin_layout Plain Layout
+Approximation Problem:
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Description
-Construction\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<4->
+4-
 \end_layout
 
 \end_inset
 
-Construct a path from 
+Construction
+\begin_inset space ~
+\end_inset
+
+Problem: Construct a path from 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -2133,23 +2097,28 @@ Construct a path from
 \end_layout
 
 \begin_layout Description
-Optimization\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<6->
+6-
 \end_layout
 
 \end_inset
 
-Construct a shortest path from 
+Optimization
+\begin_inset space ~
+\end_inset
+
+Problem: Construct a shortest path from 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -2158,28 +2127,36 @@ Construct a shortest path from
 \end_layout
 
 \begin_layout Description
-Distance\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<8->
+8-
 \end_layout
 
 \end_inset
 
-Is the distance of 
+Distance
+\begin_inset space ~
+\end_inset
+
+Problem: Is the distance of 
 \begin_inset Formula $s$
 \end_inset
 
- and\InsetSpace ~
+ and
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
 
- at most\InsetSpace ~
+ at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $d$
 \end_inset
@@ -2188,32 +2165,40 @@ Is the distance of
 \end_layout
 
 \begin_layout Description
-Approximation\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<10->
+10-
 \end_layout
 
 \end_inset
 
-Construct a path from 
+Approximation
+\begin_inset space ~
+\end_inset
+
+Problem: Construct a path from 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
 
  of length
-\newline
+\begin_inset Newline newline
+\end_inset
+
 approximately their distance.
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout Section
@@ -2226,9 +2211,9 @@ Standard Complexity Classes
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2243,225 +2228,215 @@ pgfdeclareimage[height=2cm,mask=computer-mask,interpolate=true]{computer}{beamer
 
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Classes L and NL are Defined via
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Logspace Turing Machines
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status open
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{-0.5cm}{0cm}{8cm}{5cm}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
-pgfxy(0,4)}{
-\backslash
-tape{input tape (read only), $n$ symbols}{}{3401234*3143223=}} 
-\end_layout
-
-\begin_layout Standard
-
+pgfxy(0,4)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
-uncover<2->{
+tape{input tape (read only), $n$ symbols}{}{3401234*3143223=}} 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
+\backslash
+uncover<2->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
-pgfxy(0,0.5)}{
-\backslash
-tape{}{output tape (write only)}{10690836937182}}}
+pgfxy(0,0.5)}{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+     
+\backslash
+tape{}{output tape (write only)}{10690836937182}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-  
-\backslash
-uncover<3->{
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
+\backslash
+uncover<3->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
-pgfxy(7,2)}{
+pgfxy(7,2)}{%
+\end_layout
+
+\begin_layout Plain Layout
+
+     
 \backslash
 shorttape{work tape (read/write), $O(
 \backslash
 log n)$ symbols}{}{42}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
-pgfxy(1.75,2.5)}{
+pgfxy(1.75,2.5)}{%
+\end_layout
+
+\begin_layout Plain Layout
+
+     
 \backslash
 pgfbox[center,center]{
 \backslash
 pgfuseimage{computer}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-  }
+}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
+\backslash
+color{structure}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-\end_layout
 
-\begin_layout Standard
-
-  
-\backslash
-color{structure}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  
 \backslash
 pgfsetendarrow{
 \backslash
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfxycurve(1.75,3.5)(1.75,3.75)(0,3.5)(0,3.85)
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 uncover<2->{
 \backslash
 pgfxycurve(1.75,1.5)(1.75,1)(0,1.5)(0,1.05)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 uncover<3->{
 \backslash
 pgfxycurve(2.65,2.5)(3.75,2.5)(7,1)(7,1.9)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
+\backslash
+end{pgfpicture}   
 \end_layout
 
-\begin_layout Standard
+\end_inset
 
 
-\backslash
-end{pgfpicture}   
 \end_layout
 
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
 \end_inset
 
 
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Logspace Turing Machines Are Quite Powerful
 \end_layout
 
-\begin_layout Block
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
 
-{Deterministic logspace machines can compute}
+\end_layout
+
+\begin_deeper
+\begin_layout Block
+\begin_inset Argument 2
+status collapsed
+
+\begin_layout Plain Layout
+Deterministic logspace machines can compute
 \end_layout
 
 \end_inset
@@ -2488,12 +2463,11 @@ reachability in forests.
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Non-deterministic logspace machines can compute}
+\begin_layout Plain Layout
+Non-deterministic logspace machines can compute
 \end_layout
 
 \end_inset
@@ -2515,73 +2489,86 @@ satisfiability with two literals per clause.
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
-status inlined
-
+\end_deeper
 \begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 1
+status collapsed
+
+\begin_layout Plain Layout
 
-<1>[label=hierarchy]
+1
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 3
+status collapsed
+
+\begin_layout Plain Layout
+label=hierarchy
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Complexity Class Hierarchy
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5.5cm}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetlinewidth{0.8pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 heap{5.5}{3.5}{$
 \backslash
 Class P$}{black}{1}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetdash{{2pt}}{0pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2->{
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@@ -2590,137 +2577,105 @@ heap{4.5}{3}{$
 Class{NC}^2$}{black!50!structure}{2}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 heap{3.5}{2.5}{$
 \backslash
 Class{NL}$}{black!50!structure}{3}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 heap{2.5}{2}{$
 \backslash
 Class{L}$}{black!50!structure}{4}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2->{
 \backslash
 heap{1.75}{1.5}{$
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-vphantom{A}
+vphantom{A}%
+\end_layout
+
+\begin_layout Plain Layout
+
+  
 \backslash
 smash{
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-Class{NC}^1}$}{black!50!structure}{5}}
+Class{NC}^1}$}{black!50!structure}{5}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 pgfsetdash{}{0pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2->{
 \backslash
 heap{1.1}{1}{$
 \backslash
-vphantom{A}
-\backslash
-smash{
-\backslash
-Class{AC}^0}$}{black}{6}}
+vphantom{A}%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+smash{
+\backslash
+Class{AC}^0}$}{black}{6}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetlinewidth{1.0pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{black}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfxyline(-5,0)(5,0)
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<1-2>{
 \backslash
@@ -2729,13 +2684,9 @@ langat{3.375}{$
 Lang{reach}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<1-2>{
 \backslash
@@ -2746,21 +2697,9 @@ Lang{reach}_{
 operatorname{forest}}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2>{
 \backslash
@@ -2769,13 +2708,9 @@ langat{0.975}{$
 Lang{addition}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2>{
 \backslash
@@ -2792,13 +2727,9 @@ hbox{$
 Lang{parity}$}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<3-5>{
 \backslash
@@ -2815,13 +2746,9 @@ hbox{$
 Lang{reach}$}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<4->{
 \backslash
@@ -2832,13 +2759,9 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2849,13 +2772,9 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2866,13 +2785,9 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2883,28 +2798,25 @@ operatorname{path}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
 Lang{reach}_{
 \backslash
-operatorname{path}}$}}}}
+operatorname{path}}$}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 only<5->{
 \backslash
@@ -2915,13 +2827,9 @@ Lang{reach}_{
 operatorname{tourn}}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<6->{
 \backslash
@@ -2932,13 +2840,9 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2949,13 +2853,9 @@ operatorname{tourn}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2964,43 +2864,46 @@ Lang{distance}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Standard
-
-    
+  
 \backslash
 hbox{$
 \backslash
-Lang{reach}$}}}}
+Lang{reach}$}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \backslash
 only<7->{
 \backslash
-pgfsetdash{{1pt}}{0pt}
+pgfsetdash{{1pt}}{0pt}%
+\end_layout
+
+\begin_layout Plain Layout
+
+  
 \backslash
 langat{2.375}{``$
 \backslash
 Lang{approx}_{
 \backslash
-operatorname{tourn}}$''}}
+operatorname{tourn}}$''}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3012,7 +2915,19 @@ end{pgfpicture}
 
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Circuit Complexity Classes AC
 \begin_inset Formula $^{0}$
 \end_inset
@@ -3026,15 +2941,23 @@ The Circuit Complexity Classes AC
 \end_inset
 
 
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Limit the Circuit Depth
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3043,11 +2966,7 @@ setlength
 leftmargini{1em}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3060,12 +2979,11 @@ nointerlineskip
 \end_layout
 
 \begin_layout Columns
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument 1
+status open
 
-[t]
+\begin_layout Plain Layout
+t
 \end_layout
 
 \end_inset
@@ -3079,27 +2997,15 @@ status collapsed
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{
-\end_layout
-
-\end_inset
+\begin_inset Argument 2
+status open
 
+\begin_layout Plain Layout
 Circuit Class 
 \begin_inset Formula $\Class{AC}^{0}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
@@ -3149,27 +3055,15 @@ unbounded fan-in
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{
-\end_layout
-
-\end_inset
+\begin_inset Argument 2
+status open
 
+\begin_layout Plain Layout
 Circuit Class 
 \begin_inset Formula $\Class{NC}^{1}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
@@ -3226,27 +3120,15 @@ bounded fan-in
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{
-\end_layout
-
-\end_inset
+\begin_inset Argument 2
+status open
 
+\begin_layout Plain Layout
 Circuit Class 
 \begin_inset Formula $\Class{NC}^{2}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
@@ -3279,15 +3161,16 @@ bounded fan-in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<2>
+2
 \end_layout
 
 \end_inset
@@ -3299,12 +3182,24 @@ hierarchy
 Standard Complexity Results on Finding Paths
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 All Variants of Finding Paths in Directed Graphs
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Are Equally Difficult
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}$
 \end_inset
@@ -3362,14 +3257,15 @@ the approximation problem in logspace iff
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<3>
+3
 \end_layout
 
 \end_inset
@@ -3377,12 +3273,24 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout BeginFrame
-FindingPaths in Forests and Directed Paths is Easy,
-\newline
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Finding Paths in Forests and Directed Paths is Easy,
+\begin_inset Newline newline
+\end_inset
+
 But Not Trivial
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{forest}}$
 \end_inset
@@ -3398,7 +3306,10 @@ But Not Trivial
 -complete.
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -3417,13 +3328,14 @@ But Not Trivial
 -complete.
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<4>
+4
 \end_layout
 
 \end_inset
@@ -3439,20 +3351,34 @@ Finding Paths in Tournaments
 Complexity of: Does a Path Exist?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Definition of the Tournament Reachability Problem
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
-Let 
+Let
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Lang{reach}_{\operatorname{tourn}}$
 \end_inset
 
 
-\color default
- contain all triples 
+\color none
+ 
+\color inherit
+contain all triples 
 \begin_inset Formula $(T,s,t)$
 \end_inset
 
@@ -3468,12 +3394,18 @@ Let
 \end_layout
 
 \begin_layout Enumerate
-there exists a path from\InsetSpace ~
+there exists a path from
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -3482,10 +3414,28 @@ there exists a path from\InsetSpace ~
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Tournament Reachability Problem is Very Easy
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 \begin_inset Formula $\Lang{reach}_{\operatorname{tourn}}\in\Class{AC}^{0}$
 \end_inset
@@ -3498,12 +3448,11 @@ The Tournament Reachability Problem is Very Easy
 \end_layout
 
 \begin_layout AlertBlock
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Implications}
+\begin_layout Plain Layout
+Implications
 \end_layout
 
 \end_inset
@@ -3539,14 +3488,15 @@ easier
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<5>
+5
 \end_layout
 
 \end_inset
@@ -3558,21 +3508,37 @@ hierarchy
 Complexity of: Construct a Shortest Path
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Finding a Shortest Path Is as Difficult as
-\newline
+\begin_inset Newline newline
+\end_inset
+
 the Distance Problem
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
-Let 
+Let
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
 
+
+\color none
  
-\color default
+\color inherit
 contain all tuples 
 \begin_inset Formula $(T,s,t,d)$
 \end_inset
@@ -3593,12 +3559,18 @@ the distance of
 \begin_inset Formula $s$
 \end_inset
 
- and\InsetSpace ~
+ and
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
 
- is at most\InsetSpace ~
+ is at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $d$
 \end_inset
@@ -3607,10 +3579,28 @@ the distance of
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Tournament Distance Problem is Hard
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3623,13 +3613,14 @@ The Tournament Distance Problem is Hard
 \end_layout
 
 \begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
 
-\hfill
 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3649,9 +3640,10 @@ beamerskipbutton{Skip Proof}}
 
 \begin_layout Corollary
 Shortest path in tournaments can be constructed
-\newline
-in logarithmic space, iff
- 
+\begin_inset Newline newline
+\end_inset
+
+in logarithmic space, iff 
 \begin_inset Formula $\Class{L}=\Class{NL}$
 \end_inset
 
@@ -3669,7 +3661,19 @@ in logarithmic space, iff
 .
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Proof That 
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3677,11 +3681,17 @@ Proof That
  is NL-complete
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3694,12 +3704,11 @@ nointerlineskip
 \end_layout
 
 \begin_layout Columns
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 1
+status open
 
-[t,onlytextwidth]
+\begin_layout Plain Layout
+t,onlytextwidth
 \end_layout
 
 \end_inset
@@ -3714,9 +3723,9 @@ status inlined
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3731,16 +3740,10 @@ leftmargini{1.5em}
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{
-\end_layout
-
-\end_inset
+\begin_inset Argument 2
+status open
 
+\begin_layout Plain Layout
 Reduce 
 \begin_inset Formula $\Lang{reach}$
 \end_inset
@@ -3750,12 +3753,6 @@ Reduce
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
@@ -3765,12 +3762,12 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<alert@1>
+alert@1
 \end_layout
 
 \end_inset
@@ -3787,12 +3784,12 @@ Is input
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<2-| alert@2-8>
+2-| alert@2-8
 \end_layout
 
 \end_inset
@@ -3809,18 +3806,20 @@ Map
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<9-| alert@9>
+9-| alert@9
 \end_layout
 
 \end_inset
 
 Query:
-\newline
+\begin_inset Newline newline
+\end_inset
+
 
 \begin_inset Formula $(G',s',t',3)\in\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3829,39 +3828,30 @@ Query:
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-{
-\end_layout
-
-\end_inset
+\begin_inset Argument 2
+status open
 
+\begin_layout Plain Layout
 Correctness
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<10->
+10-
 \end_layout
 
 \end_inset
@@ -3871,24 +3861,32 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<10-| alert@10-11>
+10-| alert@10-11
 \end_layout
 
 \end_inset
 
-A path in\InsetSpace ~
+A path in
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $G$
 \end_inset
 
  induces
-\newline
-a length-3 path in\InsetSpace ~
+\begin_inset Newline newline
+\end_inset
+
+a length-3 path in
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $G'$
 \end_inset
@@ -3897,24 +3895,32 @@ a length-3 path in\InsetSpace ~
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
+\begin_inset Argument item:2
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<12-| alert@12-13>
+12-| alert@12-13
 \end_layout
 
 \end_inset
 
-A length-3 path in\InsetSpace ~
+A length-3 path in
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $G'$
 \end_inset
 
  induces
-\newline
-a path in\InsetSpace ~
+\begin_inset Newline newline
+\end_inset
+
+a path in
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $G'$
 \end_inset
@@ -3929,115 +3935,75 @@ a path in\InsetSpace ~
 
 \begin_layout Example
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{0cm}{-1.25cm}{4.5cm}{3.75cm}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{A}{
 \backslash
 pgfxy(1,3.3)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{B}{
 \backslash
 pgfxy(2,3.3)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{C}{
 \backslash
 pgfxy(3,3.3)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 graphnode{D}{
 \backslash
 pgfxy(4,3.3)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{white}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4046,13 +4012,9 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$s$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4061,128 +4023,75 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$t$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfsetendarrow{
 \backslash
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodesetsepstart{2pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfnodesetsepend{2pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 alert<3>{
 \backslash
 pgfnodeconnline{B}{A}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 alert<4>{
 \backslash
 pgfnodeconnline{B}{C}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 alert<5,10-11,13>{
 \backslash
 pgfnodeconnline{C}{D}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 alert<6,10-11,13>{
 \backslash
 pgfnodeconncurve{A}{C}{45}{135}{15pt}{15pt}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-   
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4193,32 +4102,16 @@ pgfbox[left,center]{$G
 colon$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
-only<2->{
-\end_layout
-
-\begin_layout Standard
-
+only<2->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
@@ -4229,240 +4122,160 @@ pgfbox[left,center]{$G'
 colon$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{A1}{
 \backslash
 pgfxy(1,2.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{B1}{
 \backslash
 pgfxy(2,2.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{C1}{
 \backslash
 pgfxy(3,2.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{D1}{
 \backslash
 pgfxy(4,2.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{A2}{
 \backslash
 pgfxy(1,1.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{B2}{
 \backslash
 pgfxy(2,1.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{C2}{
 \backslash
 pgfxy(3,1.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{D2}{
 \backslash
 pgfxy(4,1.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{A3}{
 \backslash
 pgfxy(1,0.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{B3}{
 \backslash
 pgfxy(2,0.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{C3}{
 \backslash
 pgfxy(3,0.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{D3}{
 \backslash
 pgfxy(4,0.25)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{A4}{
 \backslash
 pgfxy(1,-.75)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{B4}{
 \backslash
 pgfxy(2,-.75)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{C4}{
 \backslash
 pgfxy(3,-.75)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 graphnode{D4}{
 \backslash
 pgfxy(4,-.75)}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-     {
+   {
 \backslash
 color{white}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-      
+    
 \backslash
 pgfputat{
 \backslash
@@ -4471,13 +4284,9 @@ pgfnodecenter{A1}}{
 pgfbox[center,center]{$s'$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-      
+    
 \backslash
 pgfputat{
 \backslash
@@ -4486,1134 +4295,684 @@ pgfnodecenter{D4}}{
 pgfbox[center,center]{$t'$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+   }
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-  }}
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+
+\backslash
+only<8->{%
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-   
+  
+\backslash
+pgfsetlinewidth{0.4pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+color{beamerexample!25!averagebackgroundcolor}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
-only<8->{
+pgfnodeconnline{A2}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfsetlinewidth{0.4pt}
+pgfnodeconnline{B2}{A1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B2}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-color{beamerexample!25!averagebackgroundcolor}
+pgfnodeconnline{B2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A2}{C1}
+pgfnodeconnline{D2}{A1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D2}{B1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A2}{D1}
+pgfnodeconnline{A3}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B2}{A1}
+pgfnodeconnline{B3}{A2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B3}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B2}{C1}
+pgfnodeconnline{B3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B2}{D1}
+pgfnodeconnline{D3}{A2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D3}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{C2}{D1}
+pgfnodeconnline{A4}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{D2}{A1}
+pgfnodeconnline{B4}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B4}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{D2}{B1}
+pgfnodeconnline{B4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A3}{C2}
+pgfnodeconnline{D4}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D4}{B3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A3}{D2}
+pgfsetstartarrow{
+\backslash
+pgfarrowto}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A1}{B1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B3}{A2}
+pgfnodeconnline{B1}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C1}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B3}{C2}
+pgfnodeconnline{A2}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B2}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B3}{D2}
+pgfnodeconnline{C2}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A3}{B3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{C3}{D2}
+pgfnodeconnline{B3}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C3}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{D3}{A2}
+pgfnodeconnline{A4}{B4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B4}{C4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{D3}{B2}
+pgfnodeconnline{C4}{D4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfclearstartarrow
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A4}{C3}
+pgfnodeconncurve{A3}{A1}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconncurve{A4}{A2}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A4}{D3}
+pgfnodeconncurve{A4}{A1}{135}{-135}{15pt}{15pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconncurve{B3}{B1}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B4}{A3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B4}{C3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B4}{D3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{C4}{D3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{D4}{A3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{D4}{B3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfsetstartarrow{
-\backslash
-pgfarrowto}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{A1}{B1}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B1}{C1}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{C1}{D1}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{A2}{B2}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B2}{C2}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{C2}{D2}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{A3}{B3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B3}{C3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{C3}{D3}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{A4}{B4}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{B4}{C4}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconnline{C4}{D4}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfclearstartarrow
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{A3}{A1}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{A4}{A2}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{A4}{A1}{135}{-135}{15pt}{15pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{B3}{B1}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{B4}{B2}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{B4}{B1}{135}{-135}{15pt}{15pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{C3}{C1}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{C4}{C2}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{C4}{C1}{135}{-135}{15pt}{15pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{D3}{D1}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{D4}{D2}{135}{-135}{10pt}{10pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfnodeconncurve{D4}{D1}{135}{-135}{15pt}{15pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-color{beamerexample}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-    
-\backslash
-pgfsetlinewidth{0.6pt}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  }
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
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+pgfnodeconncurve{C3}{C1}{135}{-135}{10pt}{10pt}
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+pgfnodeconncurve{C4}{C2}{135}{-135}{10pt}{10pt}
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+pgfnodeconncurve{C4}{C1}{135}{-135}{15pt}{15pt}
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-    
+  
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-  }
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-\begin_layout Standard
-
+pgfnodeconncurve{D4}{D1}{135}{-135}{15pt}{15pt}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
   
+\backslash
+color{beamerexample}
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-
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+pgfsetlinewidth{0.6pt}
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+}
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-
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-\begin_layout Standard
 
-    
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-\end_layout
-
-\begin_layout Standard
-
+only<3->{%
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-    
-\backslash
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+  
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- 
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+pgfnodeconnline{B1}{A2}
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+pgfnodeconnline{B2}{A3}
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+}
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-\end_layout
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-\begin_layout Standard
 
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-\begin_layout Standard
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-  } 
+  
+\backslash
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+  
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+
 
-  
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+pgfnodeconnline{A3}{C4}
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+} 
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-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-    
 \backslash
-pgfnodeconnline{B2}{B3}
+only<7->{%
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-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+color<7>{red}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
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-pgfnodeconnline{B3}{B4}
+alert<12-13>{
+\backslash
+pgfnodeconnline{A1}{A2}}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A2}{A3}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
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-pgfnodeconnline{C1}{C2}
+pgfnodeconnline{A3}{A4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B1}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
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-pgfnodeconnline{C2}{C3}
+pgfnodeconnline{B2}{B3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B3}{B4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{C3}{C4}
+pgfnodeconnline{C1}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{C2}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{D1}{D2}
+pgfnodeconnline{C3}{C4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D1}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfnodeconnline{D2}{D3}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 alert<11>{
 \backslash
 pgfnodeconnline{D3}{D4}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  }
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5625,14 +4984,15 @@ end{pgfpicture}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<6>
+6
 \end_layout
 
 \end_inset
@@ -5644,20 +5004,34 @@ hierarchy
 Complexity of: Approximating the Shortest Path
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Approximators Compute Paths that Are Nearly As Short As a Shortest Path
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
-An 
+An
+\color none
+ 
 \color red
 approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
 \end_inset
 
 
-\color default
- gets as input
+\color none
+ 
+\color inherit
+gets as input
 \end_layout
 
 \begin_deeper
@@ -5686,7 +5060,10 @@ a path from
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -5699,13 +5076,32 @@ a path from
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 There Exists a Logspace Approximation Scheme for
-\newline
-the Tournament Shortest
- Path Problem
+\begin_inset Newline newline
+\end_inset
+
+the Tournament Shortest Path Problem
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
+\begin_deeper
 \begin_layout Theorem
 There exists an approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
@@ -5716,8 +5112,10 @@ There exists an approximation scheme for
 \end_inset
 
  needs space
-\begin_inset Formula \[
-O\left(\log|V|\log\frac{1}{r-1}\right).\]
+\begin_inset Formula 
+\[
+O\left(\log|V|\log\frac{1}{r-1}\right).
+\]
 
 \end_inset
 
@@ -5733,13 +5131,14 @@ In tournaments, paths can be constructed in logarithmic space.
 \end_layout
 
 \begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
 
-\hfill
 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5753,13 +5152,14 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<7>
+7
 \end_layout
 
 \end_inset
@@ -5767,6 +5167,104 @@ status collapsed
 hierarchy
 \end_layout
 
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+If a frame includes a program listing, the frame needs to be marked as 
+\begin_inset Quotes eld
+\end_inset
+
+fragile
+\begin_inset Quotes erd
+\end_inset
+
+.
+ \SpecialChar LyX
+ has the FragileFrame layout for this.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout FragileFrame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Just a frame with a program code listing
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout FragileFrame
+This is some program code:
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset listings
+lstparams "extendedchars=true,language=Python,numbers=left,stepnumber=3,tabsize=4"
+inline false
+status open
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+    'this is a python function'
+\end_layout
+
+\begin_layout Plain Layout
+
+    pass
+\end_layout
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+'This is a German word: Tschüs'
+\end_layout
+
+\begin_layout Plain Layout
+
+pass
+\end_layout
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+'this is a python function'
+\end_layout
+
+\begin_layout Plain Layout
+
+pass
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
 \begin_layout Section*
 Summary
 \end_layout
@@ -5775,17 +5273,26 @@ Summary
 Summary
 \end_layout
 
-\begin_layout BeginFrame
-Summary
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Summary
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
+\begin_deeper
 \begin_layout Block
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Summary}
+\begin_layout Plain Layout
+Summary
 \end_layout
 
 \end_inset
@@ -5795,62 +5302,84 @@ status inlined
 
 \begin_deeper
 \begin_layout Itemize
-Tournament 
+Tournament
+\color none
+ 
 \color red
 reachability
-\color default
- is in
-\color red
+\color none
+ 
+\color inherit
+is in
+\color none
  
+\color red
+
 \begin_inset Formula $\Class{AC}^{0}$
 \end_inset
 
 
-\color default
+\color inherit
 .
  
 \end_layout
 
 \begin_layout Itemize
-There exists a 
+There exists a
+\color none
+ 
 \color red
 logspace approximation scheme
-\color default
- for 
+\color none
+ 
+\color inherit
+for
+\color none
+ 
 \color red
 approximating
-\color default
- shortest paths in tournaments.
+\color none
+ 
+\color inherit
+shortest paths in tournaments.
 \end_layout
 
 \begin_layout Itemize
-Finding 
+Finding
+\color none
+ 
 \color red
 shortest paths
-\color default
- in tournaments is
-\color red
+\color none
  
+\color inherit
+in tournaments is
+\color none
+ 
+\color red
+
 \begin_inset Formula $\Class{NL}$
 \end_inset
 
 -complete
-\color default
+\color inherit
 .
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument 2
+status collapsed
 
-{Outlook}
+\begin_layout Plain Layout
+Outlook
 \end_layout
 
 \end_inset
@@ -5861,14 +5390,18 @@ status inlined
 \begin_deeper
 \begin_layout Itemize
 The same results apply to graphs with
-\newline
+\begin_inset Newline newline
+\end_inset
+
 bounded independence number.
-\hfill
+\begin_inset space \hfill{}
+\end_inset
+
 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5884,14 +5417,18 @@ beamergotobutton{More Details}}
 
 \begin_layout Itemize
 The complexity of finding paths in undirected graphs
-\newline
+\begin_inset Newline newline
+\end_inset
+
 is partly open.
-\hfill
+\begin_inset space \hfill{}
+\end_inset
+
 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5905,20 +5442,31 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection*
 For Further Reading
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 For Further Reading
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5931,15 +5479,23 @@ beamertemplatebookbibitems
 \end_layout
 
 \begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Moon1968"
+literal "true"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {Moon1968}
-\InsetSpace ~
 John Moon.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5957,7 +5513,7 @@ Topics on Tournaments.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5969,9 +5525,9 @@ newblock
  Holt, Rinehart, and Winston, 1968.
  
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5984,15 +5540,23 @@ beamertemplatearticlebibitems
 \end_layout
 
 \begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "NickelsenT2002"
+literal "true"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {NickelsenT2002}
-\InsetSpace ~
 Arfst Nickelsen and Till Tantau.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6005,7 +5569,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6023,14 +5587,22 @@ Proc.
 \end_layout
 
 \begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Tantau2004b"
+literal "true"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {Tantau2004b}
-\InsetSpace ~
 Till Tantau 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6044,7 +5616,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6063,7 +5635,7 @@ Proc.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6075,20 +5647,17 @@ newblock
  In press.
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \start_of_appendix
 \begin_inset ERT
-status inlined
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
-AtBeginSubsection[]{} 
+AtBeginSubsection[]{}
 \end_layout
 
 \end_inset
@@ -6104,35 +5673,52 @@ Appendix
 Graphs With Bounded Independence Number
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_layout Frame
+\begin_inset Argument 3
+status collapsed
 
-[label=independence]
+\begin_layout Plain Layout
+label=independence
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Definition of Independence Number of a Graph
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
-The 
+The
+\color none
+ 
 \color red
 independence number
-\color default
+\color none
  
+\color inherit
+
 \begin_inset Formula $\alpha(G)$
 \end_inset
 
  of a directed graph
-\newline
+\begin_inset Newline newline
+\end_inset
+
 is the maximum number of vertices we can pick,
-\newline
-such that
- there is no edge between them.
+\begin_inset Newline newline
+\end_inset
+
+such that there is no edge between them.
 \end_layout
 
 \begin_layout Example
@@ -6140,26 +5726,57 @@ Tournaments have independence number 1.
  
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Results for Tournaments also Apply to
-\newline
-Graphs With Bounded Independence
- Number
+\begin_inset Newline newline
+\end_inset
+
+Graphs With Bounded Independence Number
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, 
+,
+\color none
+ 
 \color red
 reachability
-\color default
- in graphs with independence number
-\newline
-at most\InsetSpace ~
+\color none
+ 
+\color inherit
+in graphs with independence number
+\begin_inset Newline newline
+\end_inset
+
+at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6171,22 +5788,35 @@ at most\InsetSpace ~
 .
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, there exists a 
+, there exists a
+\color none
+ 
 \color red
 logspace approximation scheme
-\color default
- for approximating the shortest path in graphs with independence number
- at most\InsetSpace ~
+\color none
+ 
+\color inherit
+for approximating the shortest path in graphs with independence number at
+ most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6194,56 +5824,95 @@ logspace approximation scheme
 
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, finding the 
+, finding the
+\color none
+ 
 \color red
 shortest path
-\color default
- in graphs with independence number at most\InsetSpace ~
+\color none
+ 
+\color inherit
+in graphs with independence number at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
- is 
+ is
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Class{NL}$
 \end_inset
 
 -complete
-\color default
+\color inherit
 .
 \end_layout
 
+\end_deeper
 \begin_layout Subsection
 Finding Paths in Undirected Graphs
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
-status inlined
+\begin_layout Frame
+\begin_inset Argument 1
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-<1-2>[label=undirected]
+1-2
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 3
+status collapsed
+
+\begin_layout Plain Layout
+label=undirected
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Complexity of Finding Paths in Undirected Graphs
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Is Party Unknown.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{undirected}}$
 \end_inset
@@ -6270,20 +5939,44 @@ the reachability problem in logspace iff
 
 \begin_layout Itemize
 the construction problem in logspace iff 
-\begin_inset ERT
-status inlined
+\begin_inset Flex Alternative
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+1
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 2
+status open
+
+\begin_layout Plain Layout
+?
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Alert
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Class L=\Class{SL}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
 
 
-\backslash
-alt<1>{?}{
-\backslash
-alert{$
-\backslash
-Class L = 
-\backslash
-Class{SL}$}}
 \end_layout
 
 \end_inset
@@ -6293,20 +5986,44 @@ Class{SL}$}}
 
 \begin_layout Itemize
 the optimization problem in logspace iff 
-\begin_inset ERT
-status inlined
+\begin_inset Flex Alternative
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+
+1
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 2
+status open
+
+\begin_layout Plain Layout
+?
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Alert
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Class L=\Class{NL}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
 
 
-\backslash
-alt<1>{?}{
-\backslash
-alert{$
-\backslash
-Class L = 
-\backslash
-Class{NL}$}}
 \end_layout
 
 \end_inset
@@ -6319,25 +6036,36 @@ the approximation problem in logspace iff ?.
  
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection
 The Approximation Scheme is Optimal
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_layout Frame
+\begin_inset Argument 3
+status collapsed
 
-[label=optimality]
+\begin_layout Plain Layout
+label=optimality
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 The Approximation Scheme is Optimal
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 Suppose there exists an approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
@@ -6362,7 +6090,9 @@ Suppose there exists an approximation scheme for
 \begin_deeper
 \begin_layout Enumerate
 Suppose the approximation scheme exists.
-\newline
+\begin_inset Newline newline
+\end_inset
+
 We show 
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}\in\Class{DSPACE}\bigl[\log^{2-\epsilon}n\bigr]$
 \end_inset
@@ -6390,7 +6120,9 @@ Run the approximation scheme for
 \end_inset
 
 .
-\newline
+\begin_inset Newline newline
+\end_inset
+
 This needs space 
 \begin_inset Formula $\smash{O(\log^{2-\epsilon}n)}$
 \end_inset
@@ -6404,7 +6136,7 @@ The resulting path has optimal length.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6417,9 +6149,6 @@ qedhere
 \end_layout
 
 \end_deeper
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \end_body
 \end_document