Whitespace cosmetics

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

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 06649dd8214c88bbf458c46e0bfe481d1534b125..0a6e9c2e133f63eed323fbfb0de696b1d478d263 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,7 +1,9 @@
-#LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#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}
@@ -150,40 +152,73 @@
 \end_preamble
 \options notes=show
 \use_default_options false
+\maintain_unincluded_children false
 \language english
+\language_package default
 \inputencoding auto
-\font_roman times
-\font_sans default
-\font_typewriter default
+\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
-\font_tt_scale 100
-
+\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_esint 0
+\use_geometry true
+\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
+\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 false
-\author "" 
-\author "" 
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
 \end_header
 
 \begin_body
@@ -201,12 +236,12 @@ Till Tantau
 \end_layout
 
 \begin_layout Institute
-International Computer Schience Institute
+International Computer Science Institute
 \begin_inset Newline newline
 \end_inset
 
 Berkeley, California
-\begin_inset OptArg
+\begin_inset Argument 1
 status collapsed
 
 \begin_layout Plain Layout
@@ -222,10 +257,20 @@ 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 CommandInset toc
 LatexCommand tableofcontents
@@ -246,13 +291,10 @@ status collapsed
 
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \begin_inset ERT
-status collapsed
+status open
 
 \begin_layout Plain Layout
 
@@ -261,26 +303,14 @@ status collapsed
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
 % of every subsection.
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
 
 \backslash
-AtBeginSubsection[]{
-\end_layout
-
-\begin_layout Plain Layout
-
+AtBeginSubsection[]{%
 \end_layout
 
 \begin_layout Plain Layout
@@ -292,10 +322,6 @@ frame<handout:0>{
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 frametitle{Outline}   
@@ -303,19 +329,11 @@ frametitle{Outline}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 tableofcontents[current,currentsubsection] 
 \end_layout
 
-\begin_layout Plain Layout
-
-\end_layout
-
 \begin_layout Plain Layout
 
   }
@@ -323,10 +341,6 @@ tableofcontents[current,currentsubsection]
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
 }
 \end_layout
 
@@ -343,10 +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
@@ -369,90 +393,78 @@ begin{pgfpicture}{1.25cm}{-1cm}{7cm}{4cm}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfnodebox{A}[virtual]{
 \backslash
-pgfxy(2,1)}{
-\backslash
-pgfuseimage{knight1}}{2pt}{2pt}
+pgfxy(2,1)}{%
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight1}}{2pt}{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-  
+
 \backslash
 pgfnodebox{B}[virtual]{
 \backslash
-pgfxy(6,1)}{
-\backslash
-pgfuseimage{knight2}}{2pt}{2pt}
+pgfxy(6,1)}{%
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight2}}{2pt}{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-  
+
 \backslash
 pgfnodebox{C}[virtual]{
 \backslash
-pgfxy(4,-1)}{
-\backslash
-pgfuseimage{knight3}}{2pt}{2pt}
+pgfxy(4,-1)}{%
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight3}}{2pt}{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-  
+
 \backslash
 pgfnodebox{D}[virtual]{
 \backslash
-pgfxy(4,3)}{
-\backslash
-pgfuseimage{knight4}}{2pt}{2pt}
-\end_layout
-
-\begin_layout Plain Layout
-
+pgfxy(4,3)}{%
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfuseimage{knight4}}{2pt}{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 only<3->{
 \backslash
@@ -463,17 +475,9 @@ pgfarrowto}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
-only<2->{
-\end_layout
-
-\begin_layout Plain Layout
-
+only<2->{%
 \end_layout
 
 \begin_layout Plain Layout
@@ -485,10 +489,6 @@ pgfsetlinewidth{0.6pt}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 pgfnodeconnline{A}{B}
@@ -496,10 +496,6 @@ pgfnodeconnline{A}{B}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 pgfnodeconnline{A}{C}
@@ -507,10 +503,6 @@ pgfnodeconnline{A}{C}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 pgfnodeconnline{D}{A}
@@ -518,10 +510,6 @@ pgfnodeconnline{D}{A}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 pgfnodeconnline{C}{B}
@@ -529,10 +517,6 @@ pgfnodeconnline{C}{B}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
 pgfnodeconnline{B}{D}
@@ -540,17 +524,14 @@ pgfnodeconnline{B}{D}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
     
 \backslash
-pgfnodeconnline{C}{D}}
+pgfnodeconnline{C}{D}
 \end_layout
 
 \begin_layout Plain Layout
 
+}
 \end_layout
 
 \begin_layout Plain Layout
@@ -570,12 +551,11 @@ end{pgfpicture}
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{What is a Tournament?}
+What is a Tournament?
 \end_layout
 
 \end_inset
@@ -585,12 +565,11 @@ status collapsed
 
 \begin_deeper
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<1->
+1-
 \end_layout
 
 \end_inset
@@ -599,12 +578,11 @@ A group of knights.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<2->
+2-
 \end_layout
 
 \end_inset
@@ -613,12 +591,11 @@ Every pair has a joust.
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<3->
+3-
 \end_layout
 
 \end_inset
@@ -628,10 +605,28 @@ 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
@@ -654,33 +649,21 @@ begin{pgfpicture}{1.5cm}{-1cm}{6.5cm}{4cm}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{A}{
 \backslash
@@ -689,11 +672,7 @@ pgfxy(2.5,1)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{B}{
 \backslash
@@ -702,11 +681,7 @@ pgfxy(5.5,1)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{C}{
 \backslash
@@ -715,11 +690,7 @@ pgfxy(4,-0.5)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{D}{
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@@ -728,30 +699,14 @@ pgfxy(4,2.5)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{white}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -762,11 +717,7 @@ pgfbox[center,center]{$v_2$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -777,11 +728,7 @@ pgfbox[center,center]{$v_3$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -792,11 +739,7 @@ pgfbox[center,center]{$v_4$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
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@@ -807,30 +750,14 @@ pgfbox[center,center]{$v_1$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfsetendarrow{
 \backslash
@@ -839,98 +766,62 @@ pgfarrowto}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 pgfnodesetsepstart{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
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-  
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-\end_layout
-
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-  
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-  
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-\end_layout
-
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-  
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
-\end_layout
 
-\begin_layout Plain Layout
-
-  
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 pgfnodeconnline{D}{C}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
 
 \backslash
 end{pgfpicture} 
@@ -946,12 +837,11 @@ end{pgfpicture}
 \end_layout
 
 \begin_layout Definition
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
 \begin_layout Plain Layout
-
-<2->
+2-
 \end_layout
 
 \end_inset
@@ -982,27 +872,44 @@ any two different vertices.
 
 \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 Plain Layout
-
-[<+>]
++
 \end_layout
 
 \end_inset
 
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Tournaments Arise Naturally in Different Situations
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout ExampleBlock
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Applicatins in Ordering Theory}
+Applications in Ordering Theory
 \end_layout
 
 \end_inset
@@ -1021,17 +928,19 @@ 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
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Applications in Sociology}
+Applications in Sociology
 \end_layout
 
 \end_inset
@@ -1050,17 +959,19 @@ 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
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Applications in Structural Complexity Theory}
+Applications in Structural Complexity Theory
 \end_layout
 
 \end_inset
@@ -1089,110 +1000,154 @@ 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
 
-\begin_layout Block
-\begin_inset ERT
-status collapsed
+\end_inset
 
-\begin_layout Plain Layout
 
-{
-\backslash
-strut Input for 
-\backslash
-ignorespaces
-\backslash
-def
-\backslash
-par{}% because LyX inserts superfluous paragraphs
 \end_layout
 
+\begin_deeper
+\begin_layout Block
+\begin_inset Argument 2
+status open
+
 \begin_layout Plain Layout
+Input for 
+\begin_inset Flex Only
+status open
 
-\end_layout
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
+1
+\end_layout
 
+\end_inset
 
-\backslash
-only<1>{Path Finding Problems}
-\backslash
-ignorespaces
+Path Finding Problems
 \end_layout
 
+\end_inset
+
+
+\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 Plain Layout
+\end_inset
 
 
-\backslash
-only<2-3>{$
-\backslash
-Lang{reach}$}
-\backslash
-ignorespaces
-\end_layout
+\begin_inset Formula $\Lang{reach}$
+\end_inset
 
-\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Plain Layout
+\end_inset
 
 
-\backslash
-only<4-5>{the Construction Problem}
-\backslash
-ignorespaces
-\end_layout
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
+4-5
+\end_layout
+
+\end_inset
 
+the Construction Problem
 \end_layout
 
+\end_inset
+
+
+\begin_inset Flex Only
+status open
+
 \begin_layout Plain Layout
+\begin_inset Argument 1
+status open
 
+\begin_layout Plain Layout
+6-7
+\end_layout
 
-\backslash
-only<6-7>{the Optimization Problem}
-\backslash
-ignorespaces
+\end_inset
+
+the Optimization Problem
 \end_layout
 
+\end_inset
+
+
+\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 Plain Layout
+\end_inset
+
+
+\begin_inset Formula $\Lang{distance}$
+\end_inset
 
 
-\backslash
-only<8-9>{$
-\backslash
-Lang{distance}$}
-\backslash
-ignorespaces
 \end_layout
 
+\end_inset
+
+
+\begin_inset Flex Only
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
+
 \begin_layout Plain Layout
+10-
+\end_layout
+
+\end_inset
 
+the Approximation Problem
 \end_layout
 
-\begin_layout Plain Layout
+\end_inset
 
 
-\backslash
-only<10->{the Approximation Problem}}
 \end_layout
 
 \end_inset
@@ -1242,12 +1197,11 @@ target
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<only@-9| visible@8->
+only@-9| visible@8-
 \end_layout
 
 \end_inset
@@ -1283,12 +1237,11 @@ phantom{p}
 \end_layout
 
 \begin_layout Itemize
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<only@10->
+only@10-
 \end_layout
 
 \end_inset
@@ -1326,19 +1279,25 @@ 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 collapsed
+\end_inset
 
-\begin_layout Plain Layout
 
+\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
@@ -1346,36 +1305,59 @@ onslide<1,3,5,7,9,11-12>
 
 \end_layout
 
-\begin_layout Columns
-\begin_inset ERT
-status collapsed
+\begin_deeper
+\begin_layout Standard
+\begin_inset Flex Alternative
+status open
 
 \begin_layout Plain Layout
+\begin_inset Argument 1
+status open
 
-[t,onlytextwidth]
+\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 collapsed
+status open
 
 \begin_layout Plain Layout
 
 
-\backslash
-alt<1-2>{
 \backslash
 column{
 \backslash
-textwidth}}{
+textwidth}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
 \backslash
-column{5cm}}
+column{5cm}
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -1384,12 +1366,11 @@ column{5cm}}
 \end_layout
 
 \begin_layout ExampleBlock
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Example Input}
+Example Input
 \end_layout
 
 \end_inset
@@ -1729,16 +1710,33 @@ 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 collapsed
+status open
 
 \begin_layout Plain Layout
 
 
 \backslash
-only<3->{
-\backslash
-column{5cm}}
+column{5cm}
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -1747,12 +1745,21 @@ column{5cm}}
 \end_layout
 
 \begin_layout ExampleBlock
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
 \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
@@ -1774,44 +1781,28 @@ begin{pgfpicture}{2.5cm}{-0.6cm}{7.5cm}{2.6cm}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
-only<5-8,10->{
-\end_layout
-
-\begin_layout Plain Layout
-
+only<5-8,10->{%
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{A}{
 \backslash
@@ -1820,11 +1811,7 @@ pgfxy(3,1)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{B}{
 \backslash
@@ -1833,11 +1820,7 @@ pgfxy(5,1)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{C}{
 \backslash
@@ -1846,11 +1829,7 @@ pgfxy(4,0)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{D}{
 \backslash
@@ -1859,30 +1838,14 @@ pgfxy(4,2)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 color{white}
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfputat{
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@@ -1893,11 +1856,7 @@ pgfbox[center,center]{$t$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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@@ -1908,30 +1867,14 @@ pgfbox[center,center]{$s$}}
 
 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfsetendarrow{
 \backslash
@@ -1940,42 +1883,21 @@ pgfarrowto}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
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 pgfnodesetsepstart{2pt}
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
-
-                      
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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@@ -1984,11 +1906,7 @@ pgfnodeconnline{A}{B}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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@@ -1997,11 +1915,7 @@ pgfnodeconnline{A}{C}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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@@ -2010,11 +1924,7 @@ pgfnodeconnline{D}{A}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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@@ -2023,42 +1933,26 @@ pgfnodeconnline{C}{B}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
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+}
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@@ -2089,15 +1979,13 @@ end{pgfpicture}
 
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 \end_deeper
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-\begin_inset ERT
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+\end_deeper
+\begin_layout Overprint
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-
-
-\backslash
-onslide<2,4,6,8,10>
+2,4,6,8,10
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 \end_inset
@@ -2105,13 +1993,13 @@ onslide<2,4,6,8,10>
 
 \end_layout
 
+\begin_deeper
 \begin_layout Block
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Variants of Path Finding Problems}
+Variants of Path Finding Problems
 \end_layout
 
 \end_inset
@@ -2120,39 +2008,21 @@ status collapsed
 \end_layout
 
 \begin_deeper
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-\begin_inset ERT
-status collapsed
+\begin_layout Description
+\begin_inset Argument item:1
+status open
 
 \begin_layout Plain Layout
-
-
-\backslash
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+2-
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-
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-
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-Problem: 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-<2->
-\end_layout
-
-\end_inset
-
-Is there a path from 
+Problem: Is there a path from 
 \begin_inset Formula $s$
 \end_inset
 
@@ -2165,25 +2035,33 @@ Is there a path from
 \end_inset
 
 ?
+\begin_inset Argument 2
+status open
+
+\begin_layout Plain Layout
+Approximation Problem:
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-\begin_layout Description
-Construction
-\begin_inset space ~
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-Problem: 
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-status collapsed
 
-\begin_layout Plain Layout
+\end_layout
+
+\begin_layout Description
+\begin_inset Argument item:1
+status open
 
-<4->
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+4-
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 \end_inset
 
-Construct a path from 
+Construction
+\begin_inset space ~
+\end_inset
+
+Problem: Construct a path from 
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 \end_inset
 
@@ -2199,22 +2077,20 @@ Construct a path from
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 \begin_layout Description
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-\end_inset
-
-Problem: 
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-status collapsed
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 \begin_layout Plain Layout
-
-<6->
+6-
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 \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
 
@@ -2230,22 +2106,20 @@ Construct a shortest path from
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 \begin_layout Description
-Distance
-\begin_inset space ~
-\end_inset
-
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
 \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
 
@@ -2269,22 +2143,20 @@ Is the distance of
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 \begin_layout Description
-Approximation
-\begin_inset space ~
-\end_inset
-
-Problem: 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:1
+status open
 
 \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
 
@@ -2303,6 +2175,7 @@ Construct a path from
 approximately their distance.
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout Section
@@ -2332,7 +2205,11 @@ 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
 \begin_inset Newline newline
 \end_inset
@@ -2340,9 +2217,15 @@ The Classes L and NL are Defined via
 Logspace Turing Machines
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status open
+status collapsed
 
 \begin_layout Plain Layout
 
@@ -2353,67 +2236,67 @@ begin{pgfpicture}{-0.5cm}{0cm}{8cm}{5cm}
 
 \begin_layout Plain Layout
 
+
+\backslash
+pgfputat{
+\backslash
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 \end_layout
 
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-\backslash
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-\backslash
-pgfxy(0,4)}{
 \backslash
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 \begin_layout Plain Layout
 
+
+\backslash
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 \begin_layout Plain Layout
 
   
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-uncover<2->{
+pgfputat{
+\backslash
+pgfxy(0,0.5)}{%
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 \begin_layout Plain Layout
 
+     
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-    
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-\backslash
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-\backslash
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+}
 \end_layout
 
 \begin_layout Plain Layout
 
+
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+uncover<3->{%
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 \begin_layout Plain Layout
 
   
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-uncover<3->{
-\end_layout
-
-\begin_layout Plain Layout
-
+pgfputat{
+\backslash
+pgfxy(7,2)}{%
 \end_layout
 
 \begin_layout Plain Layout
 
-    
-\backslash
-pgfputat{
-\backslash
-pgfxy(7,2)}{
+     
 \backslash
 shorttape{work tape (read/write), $O(
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@@ -2422,15 +2305,16 @@ log n)$ symbols}{}{42}}
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfputat{
+\backslash
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 \end_layout
 
 \begin_layout Plain Layout
 
-    
-\backslash
-pgfputat{
-\backslash
-pgfxy(1.75,2.5)}{
+     
 \backslash
 pgfbox[center,center]{
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+}
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
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-
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-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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@@ -2491,22 +2351,14 @@ pgfarrowto}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 uncover<2->{
 \backslash
@@ -2515,11 +2367,7 @@ pgfxycurve(1.75,1.5)(1.75,1)(0,1.5)(0,1.05)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 uncover<3->{
 \backslash
@@ -2528,31 +2376,44 @@ pgfxycurve(2.65,2.5)(3.75,2.5)(7,1)(7,1.9)}
 
 \begin_layout Plain Layout
 
+
+\backslash
+end{pgfpicture}   
 \end_layout
 
-\begin_layout Plain Layout
+\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
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Deterministic logspace machines can compute}
+Deterministic logspace machines can compute
 \end_layout
 
 \end_inset
@@ -2579,12 +2440,11 @@ reachability in forests.
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Non-deterministic logspace machines can compute}
+Non-deterministic logspace machines can compute
 \end_layout
 
 \end_inset
@@ -2606,20 +2466,48 @@ satisfiability with two literals per clause.
 \end_layout
 
 \end_deeper
-\begin_layout BeginFrame
-\begin_inset ERT
+\end_deeper
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+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
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 status collapsed
 
 \begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
 
-<1>[label=hierarchy]
+
+\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 collapsed
@@ -2633,22 +2521,14 @@ begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5.5cm}
 
 \begin_layout Plain Layout
 
-\end_layout
-
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-  
 \backslash
 pgfsetlinewidth{0.8pt}
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 heap{5.5}{3.5}{$
 \backslash
@@ -2657,22 +2537,14 @@ Class P$}{black}{1}
 
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-\begin_layout Plain Layout
 
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 \backslash
 pgfsetdash{{2pt}}{0pt}
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 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 only<2->{
 \backslash
@@ -2683,11 +2555,7 @@ Class{NC}^2$}{black!50!structure}{2}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 heap{3.5}{2.5}{$
 \backslash
@@ -2696,11 +2564,7 @@ Class{NL}$}{black!50!structure}{3}
 
 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
 
-  
 \backslash
 heap{2.5}{2}{$
 \backslash
@@ -2709,109 +2573,85 @@ Class{L}$}{black!50!structure}{4}
 
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-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 only<2->{
 \backslash
 heap{1.75}{1.5}{$
 \backslash
-vphantom{A}
+vphantom{A}%
+\end_layout
+
+\begin_layout Plain Layout
+
+  
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+Class{NC}^1}$}{black!50!structure}{5}
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+}
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 \begin_layout Plain Layout
 
-  
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 \backslash
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 \backslash
-vphantom{A}
-\backslash
-smash{
-\backslash
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+vphantom{A}%
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 \begin_layout Plain Layout
 
+  
+\backslash
+smash{
+\backslash
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 \begin_layout Plain Layout
 
+}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
 
-  
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
-
-\end_layout
-
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-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 only<1-2>{
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@@ -2822,11 +2662,7 @@ Lang{reach}$}}
 
 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
 
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-
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-
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 \begin_layout Plain Layout
 
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-
-\begin_layout Plain Layout
 
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 \backslash
 only<4->{
 \backslash
@@ -2925,11 +2737,7 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2942,11 +2750,7 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2959,11 +2763,7 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -2976,26 +2776,23 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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 \backslash
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 \backslash
-operatorname{path}}$}}}}
+operatorname{path}}$}}}
 \end_layout
 
 \begin_layout Plain Layout
 
+}
 \end_layout
 
 \begin_layout Plain Layout
 
-  
+
 \backslash
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-\end_layout
-
-\begin_layout Plain Layout
 
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 \backslash
 only<6->{
 \backslash
@@ -3025,11 +2818,7 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 hbox{$
 \backslash
@@ -3042,11 +2831,7 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
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 \backslash
@@ -3057,38 +2842,41 @@ ignorespaces
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 hbox{$
 \backslash
-Lang{reach}$}}}}
+Lang{reach}$}}}
 \end_layout
 
 \begin_layout Plain Layout
 
+}
 \end_layout
 
 \begin_layout Plain Layout
 
-  
+
 \backslash
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 \backslash
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-\backslash
+pgfsetdash{{1pt}}{0pt}%
+\end_layout
+
+\begin_layout Plain Layout
+
+  
+\backslash
 langat{2.375}{``$
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 \backslash
-operatorname{tourn}}$''}}
+operatorname{tourn}}$''}
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 \begin_layout Plain Layout
 
+}
 \end_layout
 
 \begin_layout Plain Layout
@@ -3103,7 +2891,19 @@ 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
@@ -3123,6 +2923,12 @@ The Circuit Complexity Classes AC
 Limit the Circuit Depth
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -3138,10 +2944,6 @@ leftmargini{1em}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
 
 \backslash
 nointerlineskip 
@@ -3153,12 +2955,11 @@ nointerlineskip
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 \begin_layout Columns
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
-
-[t]
+t
 \end_layout
 
 \end_inset
@@ -3172,27 +2973,15 @@ status collapsed
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
 Circuit Class 
 \begin_inset Formula $\Class{AC}^{0}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
 \end_layout
 
 \end_inset
@@ -3242,27 +3031,15 @@ unbounded fan-in
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
 Circuit Class 
 \begin_inset Formula $\Class{NC}^{1}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
 \end_layout
 
 \end_inset
@@ -3319,27 +3096,15 @@ bounded fan-in
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
 Circuit Class 
 \begin_inset Formula $\Class{NC}^{2}$
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
 \end_layout
 
 \end_inset
@@ -3372,15 +3137,15 @@ 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 Plain Layout
-
-<2>
+2
 \end_layout
 
 \end_inset
@@ -3392,7 +3157,11 @@ 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
 \begin_inset Newline newline
 \end_inset
@@ -3400,6 +3169,12 @@ All Variants of Finding Paths in Directed Graphs
 Are Equally Difficult
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}$
 \end_inset
@@ -3457,14 +3232,14 @@ 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 Plain Layout
-
-<3>
+3
 \end_layout
 
 \end_inset
@@ -3472,14 +3247,24 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout BeginFrame
-FindingPaths in Forests and Directed Paths is Easy,
+\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
@@ -3495,7 +3280,10 @@ But Not Trivial
 -complete.
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -3514,13 +3302,13 @@ But Not Trivial
 -complete.
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
 \begin_layout Plain Layout
-
-<4>
+4
 \end_layout
 
 \end_inset
@@ -3536,10 +3324,20 @@ 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
@@ -3589,10 +3387,28 @@ there exists 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
 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
@@ -3605,12 +3421,11 @@ The Tournament Reachability Problem is Very Easy
 \end_layout
 
 \begin_layout AlertBlock
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Implications}
+Implications
 \end_layout
 
 \end_inset
@@ -3646,14 +3461,14 @@ easier
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
-
-<5>
+5
 \end_layout
 
 \end_inset
@@ -3665,7 +3480,11 @@ 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
 \begin_inset Newline newline
 \end_inset
@@ -3673,6 +3492,12 @@ Finding a Shortest Path Is as Difficult as
 the Distance Problem
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Definition
 Let
 \color none
@@ -3726,10 +3551,28 @@ 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
@@ -3790,7 +3633,19 @@ 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
@@ -3798,6 +3653,12 @@ Proof That
  is NL-complete
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -3815,12 +3676,11 @@ nointerlineskip
 \end_layout
 
 \begin_layout Columns
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
-
-[t,onlytextwidth]
+t,onlytextwidth
 \end_layout
 
 \end_inset
@@ -3852,16 +3712,10 @@ leftmargini{1.5em}
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
 Reduce 
 \begin_inset Formula $\Lang{reach}$
 \end_inset
@@ -3871,12 +3725,6 @@ Reduce
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
 \end_layout
 
 \end_inset
@@ -3886,12 +3734,11 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<alert@1>
+alert@1
 \end_layout
 
 \end_inset
@@ -3908,12 +3755,11 @@ Is input
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<2-| alert@2-8>
+2-| alert@2-8
 \end_layout
 
 \end_inset
@@ -3930,12 +3776,11 @@ Map
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<9-| alert@9>
+9-| alert@9
 \end_layout
 
 \end_inset
@@ -3952,39 +3797,29 @@ 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_inset Argument 2
+status open
 
 \begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
 Correctness
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
 \end_layout
 
 \end_inset
 
 
-\begin_inset ERT
-status collapsed
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
-
-<10->
+10-
 \end_layout
 
 \end_inset
@@ -3994,12 +3829,11 @@ status collapsed
 
 \begin_deeper
 \begin_layout Enumerate
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<10-| alert@10-11>
+10-| alert@10-11
 \end_layout
 
 \end_inset
@@ -4028,12 +3862,11 @@ a length-3 path in
 \end_layout
 
 \begin_layout Enumerate
-\begin_inset ERT
-status collapsed
+\begin_inset Argument item:2
+status open
 
 \begin_layout Plain Layout
-
-<12-| alert@12-13>
+12-| alert@12-13
 \end_layout
 
 \end_inset
@@ -4079,33 +3912,21 @@ begin{pgfpicture}{0cm}{-1.25cm}{4.5cm}{3.75cm}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{A}{
 \backslash
@@ -4114,11 +3935,7 @@ pgfxy(1,3.3)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{B}{
 \backslash
@@ -4127,11 +3944,7 @@ pgfxy(2,3.3)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 graphnode{C}{
 \backslash
@@ -4140,11 +3953,7 @@ pgfxy(3,3.3)}
 
 \begin_layout Plain Layout
 
-\end_layout
 
-\begin_layout Plain Layout
-
-  
 \backslash
 graphnode{D}{
 \backslash
@@ -4153,30 +3962,14 @@ pgfxy(4,3.3)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{white}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4187,11 +3980,7 @@ pgfbox[center,center]{$s$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4202,30 +3991,14 @@ pgfbox[center,center]{$t$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 color{beamerexample}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfsetendarrow{
 \backslash
@@ -4234,33 +4007,21 @@ pgfarrowto}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfnodesetsepstart{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfnodesetsepend{2pt}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 alert<3>{
 \backslash
@@ -4269,11 +4030,7 @@ pgfnodeconnline{B}{A}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 alert<4>{
 \backslash
@@ -4282,11 +4039,7 @@ pgfnodeconnline{B}{C}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 alert<5,10-11,13>{
 \backslash
@@ -4295,11 +4048,7 @@ pgfnodeconnline{C}{D}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 alert<6,10-11,13>{
 \backslash
@@ -4308,20 +4057,7 @@ pgfnodeconncurve{A}{C}{45}{135}{15pt}{15pt}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-   
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
 pgfputat{
 \backslash
@@ -4334,30 +4070,14 @@ colon$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
 
-  
 \backslash
-only<2->{
+only<2->{%
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfputat{
 \backslash
@@ -4370,11 +4090,7 @@ colon$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{A1}{
 \backslash
@@ -4383,11 +4099,7 @@ pgfxy(1,2.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{B1}{
 \backslash
@@ -4396,11 +4108,7 @@ pgfxy(2,2.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{C1}{
 \backslash
@@ -4409,11 +4117,7 @@ pgfxy(3,2.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{D1}{
 \backslash
@@ -4422,19 +4126,7 @@ pgfxy(4,2.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{A2}{
 \backslash
@@ -4443,11 +4135,7 @@ pgfxy(1,1.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{B2}{
 \backslash
@@ -4456,11 +4144,7 @@ pgfxy(2,1.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{C2}{
 \backslash
@@ -4469,11 +4153,7 @@ pgfxy(3,1.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{D2}{
 \backslash
@@ -4482,11 +4162,7 @@ pgfxy(4,1.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{A3}{
 \backslash
@@ -4495,11 +4171,7 @@ pgfxy(1,0.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{B3}{
 \backslash
@@ -4508,11 +4180,7 @@ pgfxy(2,0.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{C3}{
 \backslash
@@ -4521,11 +4189,7 @@ pgfxy(3,0.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{D3}{
 \backslash
@@ -4534,11 +4198,7 @@ pgfxy(4,0.25)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{A4}{
 \backslash
@@ -4547,11 +4207,7 @@ pgfxy(1,-.75)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{B4}{
 \backslash
@@ -4560,11 +4216,7 @@ pgfxy(2,-.75)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{C4}{
 \backslash
@@ -4573,11 +4225,7 @@ pgfxy(3,-.75)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 graphnode{D4}{
 \backslash
@@ -4586,22 +4234,14 @@ pgfxy(4,-.75)}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-     {
+   {
 \backslash
 color{white}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-      
+    
 \backslash
 pgfputat{
 \backslash
@@ -4612,11 +4252,7 @@ pgfbox[center,center]{$s'$}}
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-      
+    
 \backslash
 pgfputat{
 \backslash
@@ -4627,1112 +4263,670 @@ pgfbox[center,center]{$t'$}}
 
 \begin_layout Plain Layout
 
+   }
 \end_layout
 
 \begin_layout Plain Layout
 
-  }}
+}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
 
-   
+\backslash
+only<8->{%
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfsetlinewidth{0.4pt}
 \end_layout
 
 \begin_layout Plain Layout
 
   
 \backslash
-only<8->{
+color{beamerexample!25!averagebackgroundcolor}
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A2}{C1}
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfsetlinewidth{0.4pt}
+pgfnodeconnline{A2}{D1}
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B2}{A1}
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
-color{beamerexample!25!averagebackgroundcolor}
+pgfnodeconnline{B2}{C1}
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{B2}{D1}
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A2}{C1}
+pgfnodeconnline{C2}{D1}
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{D2}{A1}
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{A2}{D1}
+pgfnodeconnline{D2}{B1}
 \end_layout
 
 \begin_layout Plain Layout
 
+  
+\backslash
+pgfnodeconnline{A3}{C2}
 \end_layout
 
 \begin_layout Plain Layout
 
-    
+  
 \backslash
-pgfnodeconnline{B2}{A1}
+pgfnodeconnline{A3}{D2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
-pgfnodeconnline{B2}{C1}
-\end_layout
-
-\begin_layout Plain Layout
-
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-
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-    
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-
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-    
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-    
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-
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-    
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-
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-    
-\backslash
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-
-\begin_layout Plain Layout
-
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-
-\begin_layout Plain Layout
-
-    
-\backslash
-pgfnodeconnline{A3}{D2}
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{B3}{A2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{B3}{C2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{B3}{D2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{C3}{D2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
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-
-    
+  
 \backslash
 pgfnodeconnline{D3}{A2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
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-
-    
+  
 \backslash
 pgfnodeconnline{D3}{B2}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{A4}{C3}
 \end_layout
 
 \begin_layout Plain Layout
 
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-
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-    
+  
 \backslash
 pgfnodeconnline{A4}{D3}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
-\begin_layout Plain Layout
-
-    
+  
 \backslash
 pgfnodeconnline{B4}{A3}
 \end_layout
 
 \begin_layout Plain Layout
 
-\end_layout
-
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-
-    
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-pgfnodeconnline{B4}{C3}
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-    
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-    
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-
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-    
-\backslash
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-
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-
-\end_layout
-
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-
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-
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-    
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-    
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-
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-    
-\backslash
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-
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-
-\end_layout
-
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-
-    
-\backslash
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-
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-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
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-
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-
-\end_layout
-
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-    
-\backslash
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-
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-\end_layout
-
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-    
-\backslash
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-
-\begin_layout Plain Layout
-
-\end_layout
-
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-
-    
-\backslash
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
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-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
-pgfnodeconnline{A4}{B4}
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-    
-\backslash
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
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@@ -5741,15 +4935,7 @@ pgfnodeconnline{D3}{D4}}
 
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+}
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 \begin_layout Plain Layout
@@ -5765,13 +4951,13 @@ end{pgfpicture}
 \end_layout
 
 \end_deeper
-\begin_layout AgainFrame
-\begin_inset ERT
-status collapsed
+\end_deeper
+\begin_layout AgainFrame
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
-
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+6
 \end_layout
 
 \end_inset
@@ -5783,10 +4969,20 @@ 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
@@ -5845,7 +5041,19 @@ 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
 \begin_inset Newline newline
 \end_inset
@@ -5853,6 +5061,12 @@ There Exists a Logspace Approximation Scheme for
 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 $\Lang{tournament-shortest-path}$
@@ -5863,8 +5077,10 @@ 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
 
@@ -5901,13 +5117,13 @@ beamergotobutton{More Details}}
 
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-\begin_inset ERT
+\begin_inset Argument 1
 status collapsed
 
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@@ -5915,17 +5131,12 @@ status collapsed
 hierarchy
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-
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-
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 \begin_inset Note Note
 status open
 
 \begin_layout Plain Layout
-When a frame should include a program listing, the frame needs to be marked
- as 
+If a frame includes a program listing, the frame needs to be marked as 
 \begin_inset Quotes eld
 \end_inset
 
@@ -5934,8 +5145,8 @@ fragile
 \end_inset
 
 .
- This is not yet supported by LyX, so the the frame is created using TeX
- code.
+ \SpecialChar LyX
+ has the FragileFrame layout for this.
 \end_layout
 
 \end_inset
@@ -5943,42 +5154,12 @@ fragile
 
 \end_layout
 
-\begin_layout Standard
-\begin_inset ERT
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+\begin_inset Argument 4
 status open
 
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 \end_inset
@@ -5986,14 +5167,11 @@ status collapsed
 
 \end_layout
 
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-\begin_inset space \hspace{}
-\length 5mm
-\end_inset
-
+\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"
@@ -6022,7 +5200,7 @@ def func(param):
 
 \begin_layout Plain Layout
 
-'This is a German word: Tschüß'
+'This is a German word: Tschüs'
 \end_layout
 
 \begin_layout Plain Layout
@@ -6050,22 +5228,7 @@ pass
 
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-
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 Summary
 \end_layout
@@ -6074,17 +5237,26 @@ Summary
 Summary
 \end_layout
 
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+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
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 Summary
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+
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+
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-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Summary}
+Summary
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 \end_inset
@@ -6159,17 +5331,19 @@ in tournaments is
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
 \begin_layout Block
-\begin_inset ERT
+\begin_inset Argument 2
 status collapsed
 
 \begin_layout Plain Layout
-
-{Outlook}
+Outlook
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 \end_inset
@@ -6232,18 +5406,29 @@ beamergotobutton{More Details}}
 
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+\end_deeper
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 \begin_layout Subsection*
 For Further Reading
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+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
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 For Further Reading
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+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status collapsed
+status open
 
 \begin_layout Plain Layout
 
@@ -6261,6 +5446,7 @@ beamertemplatebookbibitems
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "Moon1968"
+literal "true"
 
 \end_inset
 
@@ -6321,6 +5507,7 @@ beamertemplatearticlebibitems
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "NickelsenT2002"
+literal "true"
 
 \end_inset
 
@@ -6367,6 +5554,7 @@ Proc.
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
 key "Tantau2004b"
+literal "true"
 
 \end_inset
 
@@ -6423,20 +5611,17 @@ newblock
  In press.
 \end_layout
 
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-\end_layout
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 \begin_layout Standard
 \start_of_appendix
 \begin_inset ERT
-status collapsed
+status open
 
 \begin_layout Plain Layout
 
 
 \backslash
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+AtBeginSubsection[]{}
 \end_layout
 
 \end_inset
@@ -6452,20 +5637,30 @@ Appendix
 Graphs With Bounded Independence Number
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
+\begin_layout Frame
+\begin_inset Argument 3
 status collapsed
 
 \begin_layout Plain Layout
-
-[label=independence]
+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
@@ -6495,7 +5690,19 @@ 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
 \begin_inset Newline newline
 \end_inset
@@ -6503,6 +5710,12 @@ The Results for Tournaments also Apply to
 Graphs With Bounded Independence Number
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Theorem
 For each
 \begin_inset space ~
@@ -6539,7 +5752,10 @@ at most
 .
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -6572,7 +5788,10 @@ for approximating the shortest path in graphs with independence number at
 
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -6614,21 +5833,36 @@ in graphs with independence number at most
 .
 \end_layout
 
+\end_deeper
 \begin_layout Subsection
 Finding Paths in Undirected Graphs
 \end_layout
 
-\begin_layout BeginFrame
-\begin_inset ERT
+\begin_layout Frame
+\begin_inset Argument 1
 status collapsed
 
 \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
 \begin_inset Newline newline
 \end_inset
@@ -6636,6 +5870,12 @@ The Complexity of Finding Paths in Undirected Graphs
 Is Party Unknown.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{undirected}}$
 \end_inset
@@ -6662,20 +5902,43 @@ the reachability problem in logspace iff
 
 \begin_layout Itemize
 the construction problem in logspace iff 
-\begin_inset ERT
-status collapsed
+\begin_inset Flex Alternative
+status open
+
+\begin_layout Plain Layout
+\begin_inset Argument 1
+status open
 
 \begin_layout Plain Layout
+1
+\end_layout
+
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+
+
+\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
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 \end_layout
 
 \end_inset
@@ -6685,20 +5948,43 @@ Class{SL}$}}
 
 \begin_layout Itemize
 the optimization problem in logspace iff 
-\begin_inset ERT
-status collapsed
+\begin_inset Flex Alternative
+status open
 
 \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
@@ -6711,25 +5997,36 @@ 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
+\begin_layout Frame
+\begin_inset Argument 3
 status collapsed
 
 \begin_layout Plain Layout
-
-[label=optimality]
+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 $\Lang{tournament-shortest-path}$
@@ -6813,9 +6110,6 @@ qedhere
 \end_layout
 
 \end_deeper
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \end_body
 \end_document