revtex4-1.layout: update to latest REVTeX 4.1

[lyx.git] / lib / examples / beamerlyxexample1.lyx

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index bf172ad5a766596abed1388a72779da11c462094..b4ee35edf3ae499f0f25da244d8ef1e5351d760b 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,5 +1,5 @@
-#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 276
+#LyX 2.1 created this file. For more info see http://www.lyx.org/
+\lyxformat 474
 \begin_document
 \begin_header
 \textclass beamer
@@ -149,43 +149,77 @@
 }
 \end_preamble
 \options notes=show
+\use_default_options false
+\maintain_unincluded_children false
 \language english
+\language_package default
 \inputencoding auto
+\fontencoding global
 \font_roman times
 \font_sans default
 \font_typewriter default
+\font_math auto
 \font_default_family default
+\use_non_tex_fonts false
 \font_sc false
 \font_osf false
 \font_sf_scale 100
 \font_tt_scale 100
 \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_esint 0
+\use_package amsmath 2
+\use_package amssymb 2
+\use_package cancel 0
+\use_package esint 0
+\use_package mathdots 1
+\use_package mathtools 0
+\use_package mhchem 1
+\use_package stackrel 0
+\use_package stmaryrd 0
+\use_package undertilde 0
 \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
+\index Index
+\shortcut idx
+\color #008000
+\end_index
 \secnumdepth 2
 \tocdepth 2
 \paragraph_separation indent
-\defskip medskip
+\paragraph_indentation default
 \quotes_language english
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
 \tracking_changes false
 \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
 
@@ -194,13 +228,15 @@ 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
 
@@ -213,19 +249,31 @@ 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
 
 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [pausesections]
 \end_layout
@@ -235,86 +283,55 @@ 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
@@ -332,10 +349,20 @@ 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
@@ -347,101 +374,89 @@ 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
@@ -450,99 +465,68 @@ 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
@@ -559,12 +543,11 @@ 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
@@ -574,12 +557,11 @@ status inlined
 
 \begin_deeper
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<1->
+\begin_layout Plain Layout
+1-
 \end_layout
 
 \end_inset
@@ -588,12 +570,11 @@ A group of knights.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<2->
+\begin_layout Plain Layout
+2-
 \end_layout
 
 \end_inset
@@ -602,12 +583,11 @@ Every pair has a joust.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<3->
+\begin_layout Plain Layout
+3-
 \end_layout
 
 \end_inset
@@ -617,10 +597,25 @@ In every joust one knight wins.
 
 \end_deeper
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -632,115 +627,75 @@ 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
@@ -749,13 +704,9 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$v_2$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -764,13 +715,9 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$v_3$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -779,13 +726,9 @@ pgfnodecenter{C}}{
 pgfbox[center,center]{$v_4$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -794,131 +737,79 @@ 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
@@ -935,12 +826,11 @@ end{pgfpicture}
 \end_layout
 
 \begin_layout Definition
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
-
-<2->
+\begin_layout Plain Layout
+2-
 \end_layout
 
 \end_inset
@@ -963,33 +853,49 @@ 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
-status collapsed
+\end_deeper
+\begin_layout Separator
 
-\begin_layout Standard
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 2
+status collapsed
 
-[<+>]
+\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
@@ -1001,7 +907,9 @@ 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
 
@@ -1011,12 +919,11 @@ The comparison relation may be cyclic, however.
 \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
@@ -1027,9 +934,10 @@ 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
 
@@ -1039,12 +947,11 @@ Reviewers decide for any two candidates
 \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
@@ -1063,7 +970,9 @@ 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
@@ -1071,110 +980,154 @@ 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
@@ -1224,12 +1177,11 @@ target
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<only@-9| visible@8->
+\begin_layout Plain Layout
+only@-9| visible@8-
 \end_layout
 
 \end_inset
@@ -1240,7 +1192,10 @@ A
 \color red
 maximum distance
 \color inherit
-\InsetSpace ~
+
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $d$
 \end_inset
@@ -1249,7 +1204,7 @@ maximum distance
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1262,12 +1217,11 @@ phantom{p}
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<only@10->
+\begin_layout Plain Layout
+only@10-
 \end_layout
 
 \end_inset
@@ -1292,7 +1246,7 @@ approximation ratio
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1305,19 +1259,25 @@ nointerlineskip
 \end_layout
 
 \begin_layout Overprint
+\begin_inset Argument item:1
+status open
 
+\begin_layout Plain Layout
+1,3,5,7,9,11-12
 \end_layout
 
-\begin_deeper
-\begin_layout Standard
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
 
+\end_layout
 
-\backslash
-onslide<1,3,5,7,9,11-12>
+\begin_deeper
+\begin_layout Columns
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+t,onlytextwidth
 \end_layout
 
 \end_inset
@@ -1325,36 +1285,36 @@ onslide<1,3,5,7,9,11-12>
 
 \end_layout
 
-\begin_layout Columns
-\begin_inset ERT
-status inlined
-
+\begin_deeper
 \begin_layout Standard
+\begin_inset Flex Alternative
+status open
 
-[t,onlytextwidth]
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+1-2
 \end_layout
 
 \end_inset
 
 
-\end_layout
+\begin_inset Argument 2
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset ERT
-status inlined
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
-\backslash
-alt<1-2>{
 \backslash
 column{
 \backslash
-textwidth}}{
-\backslash
-column{5cm}}
+textwidth}
 \end_layout
 
 \end_inset
@@ -1362,13 +1322,17 @@ column{5cm}}
 
 \end_layout
 
-\begin_layout ExampleBlock
+\end_inset
+
+
 \begin_inset ERT
-status inlined
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-{Example Input}
+
+\backslash
+column{5cm}
 \end_layout
 
 \end_inset
@@ -1376,45 +1340,63 @@ status inlined
 
 \end_layout
 
-\begin_deeper
-\begin_layout Standard
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
+
+\end_layout
+
+\begin_layout ExampleBlock
+\begin_inset Argument 2
+status collapsed
+
+\begin_layout Plain Layout
+Example Input
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\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
@@ -1423,11 +1405,11 @@ graphnode{A}{
 pgfxy(3,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1436,11 +1418,11 @@ graphnode{B}{
 pgfxy(5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1449,11 +1431,11 @@ graphnode{C}{
 pgfxy(4,0)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1462,30 +1444,30 @@ 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
@@ -1496,11 +1478,11 @@ 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
@@ -1511,30 +1493,30 @@ 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
@@ -1543,107 +1525,107 @@ 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
@@ -1656,11 +1638,11 @@ 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
@@ -1673,11 +1655,11 @@ 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
@@ -1690,11 +1672,11 @@ 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
@@ -1708,16 +1690,33 @@ 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
@@ -1726,12 +1725,21 @@ 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
@@ -1742,126 +1750,82 @@ 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
@@ -1870,13 +1834,9 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$t$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfputat{
 \backslash
@@ -1885,159 +1845,94 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$s$}}
 \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{beamerexample}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfsetendarrow{
 \backslash
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfnodesetsepstart{2pt}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 pgfnodesetsepend{4pt}
 \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
 alert<7,12>{
 \backslash
 pgfnodeconnline{A}{B}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 alert<5,11>{
 \backslash
 pgfnodeconnline{A}{C}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 alert<5,7,11-12>{
 \backslash
 pgfnodeconnline{D}{A}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 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
-pgfnodeconnline{B}{D}
+pgfnodeconnline{D}{C}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
+}
 \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 Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<3,9>{
 \backslash
@@ -2050,11 +1945,7 @@ pgfbox[left,center]{
 alert{``Yes''}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2068,15 +1959,13 @@ 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
 
-\backslash
-onslide<2,4,6,8,10>
+\begin_layout Plain Layout
+2,4,6,8,10
 \end_layout
 
 \end_inset
@@ -2084,13 +1973,13 @@ 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
@@ -2099,65 +1988,67 @@ 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
 
-\backslash
-usedescriptionitemofwidthas{Approximation Problem:}
+\begin_layout Plain Layout
+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
 
-\begin_layout Description
-Construction\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
+\end_inset
 
-\begin_layout Standard
 
-<4->
 \end_layout
 
+\begin_layout Description
+\begin_inset Argument item:1
+status open
+
+\begin_layout Plain Layout
+4-
+\end_layout
+
+\end_inset
+
+Construction
+\begin_inset space ~
 \end_inset
 
-Construct a path from 
+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
@@ -2166,23 +2057,27 @@ Construct a path from
 \end_layout
 
 \begin_layout Description
-Optimization\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:1
+status open
 
-<6->
+\begin_layout Plain Layout
+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
@@ -2191,28 +2086,35 @@ Construct a shortest path from
 \end_layout
 
 \begin_layout Description
-Distance\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:1
+status open
 
-<8->
+\begin_layout Plain Layout
+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
@@ -2221,32 +2123,39 @@ Is the distance of
 \end_layout
 
 \begin_layout Description
-Approximation\InsetSpace ~
-Problem: 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument item:1
+status open
 
-<10->
+\begin_layout Plain Layout
+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
@@ -2259,9 +2168,9 @@ Standard Complexity Classes
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2276,203 +2185,176 @@ 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 Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 color{structure}
 \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
 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
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2484,17 +2366,31 @@ end{pgfpicture}
 
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\end_layout
+
+\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
@@ -2521,12 +2417,11 @@ 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
@@ -2548,73 +2443,82 @@ satisfiability with two literals per clause.
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\end_deeper
+\begin_layout Separator
 
-<1>[label=hierarchy]
 \end_layout
 
-\end_inset
+\begin_layout Frame
+\begin_inset Argument 1
+status collapsed
 
-The Complexity Class Hierarchy
+\begin_layout Plain Layout
+1
 \end_layout
 
-\begin_layout Standard
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
 
+\begin_inset Argument 3
+status collapsed
 
-\backslash
-begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5.5cm}
+\begin_layout Plain Layout
+label=hierarchy
 \end_layout
 
-\begin_layout Standard
+\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 collapsed
+
+\begin_layout Plain Layout
+
 
-  
 \backslash
-pgfsetlinewidth{0.8pt}
+begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5.5cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
+\backslash
+pgfsetlinewidth{0.8pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
+
 
-  
 \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->{
 \backslash
@@ -2623,137 +2527,105 @@ 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}{$
 \backslash
-vphantom{A}
+vphantom{A}%
+\end_layout
+
+\begin_layout Plain Layout
+
+  
 \backslash
 smash{
 \backslash
-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
@@ -2762,13 +2634,9 @@ langat{3.375}{$
 Lang{reach}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<1-2>{
 \backslash
@@ -2779,21 +2647,9 @@ 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
@@ -2802,13 +2658,9 @@ langat{0.975}{$
 Lang{addition}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<2>{
 \backslash
@@ -2825,13 +2677,9 @@ hbox{$
 Lang{parity}$}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<3-5>{
 \backslash
@@ -2848,13 +2696,9 @@ hbox{$
 Lang{reach}$}}}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<4->{
 \backslash
@@ -2865,13 +2709,9 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2882,13 +2722,9 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2899,13 +2735,9 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2916,28 +2748,25 @@ 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
@@ -2948,13 +2777,9 @@ Lang{reach}_{
 operatorname{tourn}}$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 only<6->{
 \backslash
@@ -2965,13 +2790,9 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2982,13 +2803,9 @@ operatorname{tourn}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2997,43 +2814,46 @@ Lang{distance}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
 \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
@@ -3045,7 +2865,16 @@ end{pgfpicture}
 
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -3059,15 +2888,23 @@ 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
@@ -3076,11 +2913,7 @@ setlength
 leftmargini{1em}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3093,12 +2926,11 @@ 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
@@ -3112,27 +2944,15 @@ 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
@@ -3182,27 +3002,15 @@ 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
@@ -3259,27 +3067,15 @@ 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
@@ -3312,15 +3108,15 @@ 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
-
-<2>
+\begin_layout Plain Layout
+2
 \end_layout
 
 \end_inset
@@ -3332,12 +3128,24 @@ 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
@@ -3395,14 +3203,14 @@ 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
-
-<3>
+\begin_layout Plain Layout
+3
 \end_layout
 
 \end_inset
@@ -3410,12 +3218,24 @@ 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
@@ -3450,13 +3270,13 @@ But Not Trivial
 -complete.
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
-\begin_layout Standard
-
-<4>
+\begin_layout Plain Layout
+4
 \end_layout
 
 \end_inset
@@ -3472,10 +3292,20 @@ 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
 \color none
@@ -3505,12 +3335,18 @@ contain all triples
 \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
@@ -3519,10 +3355,25 @@ there exists a path from\InsetSpace ~
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -3535,12 +3386,11 @@ 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
@@ -3576,14 +3426,14 @@ easier
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument 1
+status open
 
-<5>
+\begin_layout Plain Layout
+5
 \end_layout
 
 \end_inset
@@ -3595,12 +3445,24 @@ 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
 \color none
@@ -3634,12 +3496,18 @@ 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
@@ -3648,10 +3516,25 @@ the distance of
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -3664,13 +3547,14 @@ 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
@@ -3690,9 +3574,10 @@ 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
 
@@ -3710,7 +3595,16 @@ in logarithmic space, iff
 .
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -3718,11 +3612,17 @@ 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
@@ -3735,12 +3635,11 @@ 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
@@ -3755,9 +3654,9 @@ status inlined
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3772,16 +3671,10 @@ 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
@@ -3791,12 +3684,6 @@ Reduce
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-}
 \end_layout
 
 \end_inset
@@ -3806,12 +3693,11 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<alert@1>
+\begin_layout Plain Layout
+alert@1
 \end_layout
 
 \end_inset
@@ -3828,12 +3714,11 @@ Is input
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<2-| alert@2-8>
+\begin_layout Plain Layout
+2-| alert@2-8
 \end_layout
 
 \end_inset
@@ -3850,18 +3735,19 @@ Map
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<9-| alert@9>
+\begin_layout Plain Layout
+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
@@ -3875,34 +3761,21 @@ Query:
 \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_layout Standard
+\begin_inset Argument 1
+status open
 
-<10->
+\begin_layout Plain Layout
+10-
 \end_layout
 
 \end_inset
@@ -3912,24 +3785,31 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<10-| alert@10-11>
+\begin_layout Plain Layout
+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
@@ -3938,24 +3818,31 @@ a length-3 path in\InsetSpace ~
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
+\begin_inset Argument item:2
+status open
 
-<12-| alert@12-13>
+\begin_layout Plain Layout
+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
@@ -3970,115 +3857,75 @@ 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 Plain Layout
 
-\begin_layout Standard
 
+\backslash
+color{white}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Standard
-
-  
-\backslash
-color{white}
-\end_layout
 
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-  
 \backslash
 pgfputat{
 \backslash
@@ -4087,13 +3934,9 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$s$}}
 \end_layout
 
-\begin_layout Standard
-
-\end_layout
+\begin_layout Plain Layout
 
-\begin_layout Standard
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4102,128 +3945,75 @@ 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
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+
 
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+  
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+\backslash
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+  
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+  
+\backslash
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-    
+  
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+pgfnodeconnline{C1}{C2}
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+\begin_layout Plain Layout
 
+  
+\backslash
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+\begin_layout Plain Layout
 
-    
+  
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-pgfnodeconnline{D1}{D2}
+pgfnodeconnline{C3}{C4}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D1}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-    
+  
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 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
@@ -5666,14 +4906,14 @@ end{pgfpicture}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
+\begin_inset Argument 1
+status open
 
-<6>
+\begin_layout Plain Layout
+6
 \end_layout
 
 \end_inset
@@ -5685,10 +4925,20 @@ 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
 \color none
@@ -5731,7 +4981,10 @@ a path from
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -5744,13 +4997,29 @@ a path from
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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 $\Lang{tournament-shortest-path}$
@@ -5761,57 +5030,157 @@ 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
+
+
+\end_layout
+
+\begin_layout Pause
+
+\end_layout
+
+\begin_layout Corollary
+In tournaments, paths can be constructed in logarithmic space.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+hyperlink{optimality}{
+\backslash
+beamergotobutton{More Details}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout AgainFrame
+\begin_inset Argument 1
+status collapsed
+
+\begin_layout Plain Layout
+7
+\end_layout
+
+\end_inset
+
+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
+
+.
+ 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
 
-\end_inset
+\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 Pause
+\begin_layout Plain Layout
 
+    'this is a python function'
 \end_layout
 
-\begin_layout Corollary
-In tournaments, paths can be constructed in logarithmic space.
+\begin_layout Plain Layout
+
+    pass
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
-\hfill
+def func(param):
+\end_layout
 
-\begin_inset ERT
-status inlined
+\begin_layout Plain Layout
 
-\begin_layout Standard
+'This is a German word: Tschüs'
+\end_layout
 
+\begin_layout Plain Layout
 
-\backslash
-hyperlink{optimality}{
-\backslash
-beamergotobutton{More Details}}
+pass
 \end_layout
 
-\end_inset
-
+\begin_layout Plain Layout
 
+def func(param):
 \end_layout
 
-\begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
+\begin_layout Plain Layout
 
-\begin_layout Standard
+'this is a python function'
+\end_layout
 
-<7>
+\begin_layout Plain Layout
+
+pass
 \end_layout
 
 \end_inset
 
-hierarchy
+
 \end_layout
 
+\end_deeper
 \begin_layout Section*
 Summary
 \end_layout
@@ -5820,17 +5189,26 @@ Summary
 Summary
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Summary
 \end_layout
 
-\begin_layout Block
-\begin_inset ERT
-status inlined
+\end_inset
 
-\begin_layout Standard
 
-{Summary}
+\end_layout
+
+\begin_deeper
+\begin_layout Block
+\begin_inset Argument 2
+status collapsed
+
+\begin_layout Plain Layout
+Summary
 \end_layout
 
 \end_inset
@@ -5910,12 +5288,11 @@ in tournaments is
 \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
@@ -5926,14 +5303,18 @@ 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
@@ -5949,14 +5330,18 @@ 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
@@ -5970,20 +5355,31 @@ 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
@@ -5996,18 +5392,22 @@ beamertemplatebookbibitems
 \end_layout
 
 \begin_layout Bibliography
-
-\begin_inset LatexCommand bibitem
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
 key "Moon1968"
 
 \end_inset
-\InsetSpace ~
+
+
+\begin_inset space ~
+\end_inset
+
 John Moon.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6016,8 +5416,6 @@ newblock
 
 \end_inset
 
-
-\emph default
  
 \emph on
 Topics on Tournaments.
@@ -6027,7 +5425,7 @@ Topics on Tournaments.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6039,9 +5437,9 @@ newblock
  Holt, Rinehart, and Winston, 1968.
  
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6054,18 +5452,22 @@ beamertemplatearticlebibitems
 \end_layout
 
 \begin_layout Bibliography
-
-\begin_inset LatexCommand bibitem
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
 key "NickelsenT2002"
 
 \end_inset
-\InsetSpace ~
+
+
+\begin_inset space ~
+\end_inset
+
 Arfst Nickelsen and Till Tantau.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6078,7 +5480,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6087,9 +5489,7 @@ newblock
 
 \end_inset
 
- In
-\emph default
- 
+ In 
 \emph on
 Proc.
  of COCOON 2002
@@ -6098,17 +5498,21 @@ Proc.
 \end_layout
 
 \begin_layout Bibliography
-
-\begin_inset LatexCommand bibitem
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
 key "Tantau2004b"
 
 \end_inset
-\InsetSpace ~
+
+
+\begin_inset space ~
+\end_inset
+
 Till Tantau 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6122,7 +5526,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6131,9 +5535,7 @@ newblock
 
 \end_inset
 
- In
-\emph default
- 
+ In 
 \emph on
 Proc.
  of STACS 2004
@@ -6143,7 +5545,7 @@ Proc.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6155,20 +5557,17 @@ 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
@@ -6184,20 +5583,30 @@ 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
 \color none
@@ -6212,11 +5621,14 @@ independence number
 \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
@@ -6224,15 +5636,34 @@ Tournaments have independence number 1.
  
 \end_layout
 
-\begin_layout BeginFrame
+\end_deeper
+\begin_layout Separator
+
+\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
@@ -6246,8 +5677,13 @@ reachability
  
 \color inherit
 in graphs with independence number
-\newline
-at most\InsetSpace ~
+\begin_inset Newline newline
+\end_inset
+
+at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6264,7 +5700,10 @@ at most\InsetSpace ~
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6277,8 +5716,11 @@ logspace approximation scheme
 \color none
  
 \color inherit
-for approximating the shortest path in graphs with independence number
- at most\InsetSpace ~
+for approximating the shortest path in graphs with independence number at
+ most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6291,7 +5733,10 @@ for approximating the shortest path in graphs with independence number
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6304,7 +5749,10 @@ shortest path
 \color none
  
 \color inherit
-in graphs with independence number at most\InsetSpace ~
+in graphs with independence number at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6322,26 +5770,49 @@ in graphs with independence number at most\InsetSpace ~
 .
 \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
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 3
+status collapsed
 
-<1-2>[label=undirected]
+\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
@@ -6368,20 +5839,43 @@ 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
@@ -6391,20 +5885,43 @@ 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
@@ -6417,25 +5934,36 @@ 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 $\Lang{tournament-shortest-path}$
@@ -6460,7 +5988,9 @@ 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
@@ -6488,7 +6018,9 @@ 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
@@ -6502,7 +6034,7 @@ The resulting path has optimal length.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6515,9 +6047,6 @@ qedhere
 \end_layout
 
 \end_deeper
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \end_body
 \end_document