Restore change from OpenOffice to LibreOffice.

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

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 96c2e722decca44673271434477fe87d2043576d..a59c85925fcca9c41243e4d313f395eb6fb4a759 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,5 +1,5 @@
-#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 245
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
 \begin_document
 \begin_header
 \textclass beamer
@@ -149,35 +149,68 @@
 }
 \end_preamble
 \options notes=show
+\use_default_options false
+\maintain_unincluded_children false
 \language english
+\language_package default
 \inputencoding auto
-\fontscheme times
+\fontencoding global
+\font_roman times
+\font_sans default
+\font_typewriter default
+\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_mhchem 1
+\use_mathdots 1
 \cite_engine basic
 \use_bibtopic false
+\use_indices false
 \paperorientation portrait
+\suppress_date false
+\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 true
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
 \end_header
 
 \begin_body
 
 \begin_layout Title
 The Complexity of
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Finding Paths in Tournaments
 \end_layout
 
@@ -187,12 +220,14 @@ Till Tantau
 
 \begin_layout Institute
 International Computer Schience Institute
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Berkeley, California
-\begin_inset OptArg
+\begin_inset Argument
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 ICSI
 \end_layout
 
@@ -210,7 +245,8 @@ Outline
 \end_layout
 
 \begin_layout Standard
-\begin_inset LatexCommand \tableofcontents{}
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
 
 \end_inset
 
@@ -218,7 +254,7 @@ Outline
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [pausesections]
 \end_layout
@@ -236,78 +272,78 @@ status collapsed
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 % Show the table of contents at the beginning
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 % of every subsection.
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 AtBeginSubsection[]{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 frame<handout:0>{ 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 frametitle{Outline}   
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 tableofcontents[current,currentsubsection] 
 \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
 
 }
 \end_layout
@@ -340,20 +376,20 @@ 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
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -364,11 +400,11 @@ pgfxy(2,1)}{
 pgfuseimage{knight1}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -379,11 +415,11 @@ pgfxy(6,1)}{
 pgfuseimage{knight2}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -394,11 +430,11 @@ pgfxy(4,-1)}{
 pgfuseimage{knight3}}{2pt}{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -409,30 +445,30 @@ pgfxy(4,3)}{
 pgfuseimage{knight4}}{2pt}{2pt}
 \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
@@ -443,99 +479,99 @@ pgfsetendarrow{
 pgfarrowto}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<2->{
 \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
 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{C}{D}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -553,9 +589,9 @@ end{pgfpicture}
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {What is a Tournament?}
 \end_layout
@@ -570,7 +606,7 @@ status inlined
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <1->
 \end_layout
@@ -584,7 +620,7 @@ A group of knights.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <2->
 \end_layout
@@ -598,7 +634,7 @@ Every pair has a joust.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <3->
 \end_layout
@@ -625,42 +661,42 @@ 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
+\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
@@ -669,11 +705,11 @@ graphnode{A}{
 pgfxy(2.5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -682,11 +718,11 @@ graphnode{B}{
 pgfxy(5.5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -695,11 +731,11 @@ graphnode{C}{
 pgfxy(4,-0.5)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -708,30 +744,30 @@ graphnode{D}{
 pgfxy(4,2.5)}
 \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
@@ -742,11 +778,11 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$v_2$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -757,11 +793,11 @@ pgfnodecenter{B}}{
 pgfbox[center,center]{$v_3$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -772,11 +808,11 @@ pgfnodecenter{C}}{
 pgfbox[center,center]{$v_4$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -787,30 +823,30 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$v_1$}}
 \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
@@ -819,99 +855,99 @@ 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
 
 
 \backslash
@@ -931,18 +967,22 @@ end{pgfpicture}
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <2->
 \end_layout
 
 \end_inset
 
-A 
+A
+\color none
+ 
 \color red
 tournament
+\color none
+ 
 \color inherit
- is a
+is a
 \end_layout
 
 \begin_deeper
@@ -952,7 +992,9 @@ directed graphs,
 
 \begin_layout Enumerate
 with exactly one edge between
-\newline
+\begin_inset Newline newline
+\end_inset
+
 any two different vertices.
 \end_layout
 
@@ -962,7 +1004,7 @@ any two different vertices.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [<+>]
 \end_layout
@@ -974,9 +1016,9 @@ Tournaments Arise Naturally in Different Situations
 
 \begin_layout ExampleBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Applicatins in Ordering Theory}
 \end_layout
@@ -990,7 +1032,9 @@ 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
 
@@ -1001,9 +1045,9 @@ The comparison relation may be cyclic, however.
 
 \begin_layout ExampleBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Applications in Sociology}
 \end_layout
@@ -1016,9 +1060,10 @@ 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
 
@@ -1029,9 +1074,9 @@ Reviewers decide for any two candidates
 
 \begin_layout ExampleBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Applications in Structural Complexity Theory}
 \end_layout
@@ -1052,7 +1097,9 @@ 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
@@ -1071,9 +1118,9 @@ What Does ``Finding Paths'' Mean?
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \backslash
@@ -1086,11 +1133,11 @@ def
 par{}% because LyX inserts superfluous paragraphs
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1099,11 +1146,11 @@ only<1>{Path Finding Problems}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1114,11 +1161,11 @@ Lang{reach}$}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1127,11 +1174,11 @@ only<4-5>{the Construction Problem}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1140,11 +1187,11 @@ only<6-7>{the Optimization Problem}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1155,11 +1202,11 @@ Lang{distance}$}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1173,27 +1220,39 @@ only<10->{the Approximation Problem}}
 
 \begin_deeper
 \begin_layout Itemize
-A 
+A
+\color none
+ 
 \color red
 graph
-\color inherit
+\color none
  
+\color inherit
+
 \begin_inset Formula $G=(V,E)$
 \end_inset
 
-, a 
+, a
+\color none
+ 
 \color red
 source
-\color inherit
+\color none
  
+\color inherit
+
 \begin_inset Formula $s\in V$
 \end_inset
 
- and a 
+ and a
+\color none
+ 
 \color red
 target
-\color inherit
+\color none
  
+\color inherit
+
 \begin_inset Formula $t\in V$
 \end_inset
 
@@ -1204,18 +1263,23 @@ target
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <only@-9| visible@8->
 \end_layout
 
 \end_inset
 
-A 
+A
+\color none
+ 
 \color red
 maximum distance
 \color inherit
-\InsetSpace ~
+
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $d$
 \end_inset
@@ -1224,7 +1288,7 @@ maximum distance
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1240,18 +1304,22 @@ phantom{p}
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <only@10->
 \end_layout
 
 \end_inset
 
-An 
+An
+\color none
+ 
 \color red
 approximation ratio
-\color inherit
+\color none
  
+\color inherit
+
 \begin_inset Formula $r>1$
 \end_inset
 
@@ -1263,7 +1331,7 @@ approximation ratio
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1282,9 +1350,9 @@ nointerlineskip
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1298,9 +1366,9 @@ onslide<1,3,5,7,9,11-12>
 
 \begin_layout Columns
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [t,onlytextwidth]
 \end_layout
@@ -1313,9 +1381,9 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1335,9 +1403,9 @@ column{5cm}}
 
 \begin_layout ExampleBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Example Input}
 \end_layout
@@ -1350,42 +1418,42 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{2.5cm}{-0.6cm}{7.5cm}{2.6cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 color{beamerexample}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfsetlinewidth{0.6pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1394,11 +1462,11 @@ graphnode{A}{
 pgfxy(3,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1407,11 +1475,11 @@ graphnode{B}{
 pgfxy(5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1420,11 +1488,11 @@ graphnode{C}{
 pgfxy(4,0)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -1433,30 +1501,30 @@ 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
@@ -1467,11 +1535,11 @@ 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
@@ -1482,30 +1550,30 @@ 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
@@ -1514,107 +1582,107 @@ 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
@@ -1627,11 +1695,11 @@ 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
@@ -1644,11 +1712,11 @@ 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
@@ -1661,11 +1729,11 @@ 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
@@ -1680,9 +1748,9 @@ end{pgfpicture}
 \end_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -1698,9 +1766,9 @@ column{5cm}}
 
 \begin_layout ExampleBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <only@3->{Example Output}
 \end_layout
@@ -1713,53 +1781,53 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{2.5cm}{-0.6cm}{7.5cm}{2.6cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<5-8,10->{
 \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
@@ -1768,11 +1836,11 @@ graphnode{A}{
 pgfxy(3,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1781,11 +1849,11 @@ graphnode{B}{
 pgfxy(5,1)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1794,11 +1862,11 @@ graphnode{C}{
 pgfxy(4,0)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1807,30 +1875,30 @@ 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
@@ -1841,11 +1909,11 @@ 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
@@ -1856,30 +1924,30 @@ 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
@@ -1888,42 +1956,42 @@ 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
 
                       
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1932,11 +2000,11 @@ alert<7,12>{
 pgfnodeconnline{A}{B}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1945,11 +2013,11 @@ alert<5,11>{
 pgfnodeconnline{A}{C}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1958,11 +2026,11 @@ alert<5,7,11-12>{
 pgfnodeconnline{D}{A}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -1971,42 +2039,42 @@ alert<5,11>{
 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
@@ -2021,11 +2089,11 @@ pgfbox[left,center]{
 alert{``Yes''}}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2041,9 +2109,9 @@ end{pgfpicture}
 \end_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2057,9 +2125,9 @@ onslide<2,4,6,8,10>
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Variants of Path Finding Problems}
 \end_layout
@@ -2072,9 +2140,9 @@ status inlined
 \begin_deeper
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2087,12 +2155,15 @@ usedescriptionitemofwidthas{Approximation Problem:}
 \end_layout
 
 \begin_layout Description
-Reachability\InsetSpace ~
+Reachability
+\begin_inset space ~
+\end_inset
+
 Problem: 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <2->
 \end_layout
@@ -2103,7 +2174,10 @@ 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
@@ -2112,12 +2186,15 @@ Is there a path from
 \end_layout
 
 \begin_layout Description
-Construction\InsetSpace ~
+Construction
+\begin_inset space ~
+\end_inset
+
 Problem: 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <4->
 \end_layout
@@ -2128,7 +2205,10 @@ Construct a path from
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -2137,12 +2217,15 @@ Construct a path from
 \end_layout
 
 \begin_layout Description
-Optimization\InsetSpace ~
+Optimization
+\begin_inset space ~
+\end_inset
+
 Problem: 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <6->
 \end_layout
@@ -2153,7 +2236,10 @@ 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
@@ -2162,12 +2248,15 @@ Construct a shortest path from
 \end_layout
 
 \begin_layout Description
-Distance\InsetSpace ~
+Distance
+\begin_inset space ~
+\end_inset
+
 Problem: 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <8->
 \end_layout
@@ -2178,12 +2267,18 @@ 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
@@ -2192,12 +2287,15 @@ Is the distance of
 \end_layout
 
 \begin_layout Description
-Approximation\InsetSpace ~
+Approximation
+\begin_inset space ~
+\end_inset
+
 Problem: 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <10->
 \end_layout
@@ -2208,13 +2306,18 @@ 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
 
@@ -2230,9 +2333,9 @@ Standard Complexity Classes
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2249,7 +2352,9 @@ pgfdeclareimage[height=2cm,mask=computer-mask,interpolate=true]{computer}{beamer
 
 \begin_layout BeginFrame
 The Classes L and NL are Defined via
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Logspace Turing Machines
 \end_layout
 
@@ -2257,18 +2362,18 @@ Logspace Turing Machines
 \begin_inset ERT
 status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{-0.5cm}{0cm}{8cm}{5cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2279,22 +2384,22 @@ pgfxy(0,4)}{
 tape{input tape (read only), $n$ symbols}{}{3401234*3143223=}} 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 uncover<2->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2305,22 +2410,22 @@ pgfxy(0,0.5)}{
 tape{}{output tape (write only)}{10690836937182}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 uncover<3->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2333,11 +2438,11 @@ shorttape{work tape (read/write), $O(
 log n)$ symbols}{}{42}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2350,50 +2455,50 @@ pgfbox[center,center]{
 pgfuseimage{computer}}}
 \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
 pgfsetlinewidth{0.6pt}
 \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{structure}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2402,22 +2507,22 @@ pgfsetendarrow{
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfxycurve(1.75,3.5)(1.75,3.75)(0,3.5)(0,3.85)
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2426,11 +2531,11 @@ uncover<2->{
 pgfxycurve(1.75,1.5)(1.75,1)(0,1.5)(0,1.05)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2439,11 +2544,11 @@ uncover<3->{
 pgfxycurve(2.65,2.5)(3.75,2.5)(7,1)(7,1.9)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -2461,9 +2566,9 @@ Logspace Turing Machines Are Quite Powerful
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Deterministic logspace machines can compute}
 \end_layout
@@ -2493,9 +2598,9 @@ reachability in forests.
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Non-deterministic logspace machines can compute}
 \end_layout
@@ -2521,9 +2626,9 @@ satisfiability with two literals per clause.
 \end_deeper
 \begin_layout BeginFrame
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <1>[label=hierarchy]
 \end_layout
@@ -2535,31 +2640,31 @@ The Complexity Class Hierarchy
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
 begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5.5cm}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfsetlinewidth{0.8pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2568,22 +2673,22 @@ heap{5.5}{3.5}{$
 Class P$}{black}{1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfsetdash{{2pt}}{0pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2594,11 +2699,11 @@ heap{4.5}{3}{$
 Class{NC}^2$}{black!50!structure}{2}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2607,11 +2712,11 @@ heap{3.5}{2.5}{$
 Class{NL}$}{black!50!structure}{3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2620,11 +2725,11 @@ heap{2.5}{2}{$
 Class{L}$}{black!50!structure}{4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2639,22 +2744,22 @@ smash{
 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
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2669,60 +2774,60 @@ smash{
 Class{AC}^0}$}{black}{6}}
 \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
 pgfsetlinewidth{1.0pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 color{black}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 pgfxyline(-5,0)(5,0)
 \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
@@ -2733,11 +2838,11 @@ langat{3.375}{$
 Lang{reach}$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2750,19 +2855,19 @@ Lang{reach}_{
 operatorname{forest}}$}}
 \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
@@ -2773,11 +2878,11 @@ langat{0.975}{$
 Lang{addition}$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2796,11 +2901,11 @@ hbox{$
 Lang{parity}$}}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2819,11 +2924,11 @@ hbox{$
 Lang{reach}$}}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2836,11 +2941,11 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2853,11 +2958,11 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2870,11 +2975,11 @@ operatorname{forest}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2887,11 +2992,11 @@ operatorname{path}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2902,11 +3007,11 @@ Lang{reach}_{
 operatorname{path}}$}}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2919,11 +3024,11 @@ Lang{reach}_{
 operatorname{tourn}}$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -2936,11 +3041,11 @@ vbox{
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2953,11 +3058,11 @@ operatorname{tourn}}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2968,11 +3073,11 @@ Lang{distance}$,}
 ignorespaces
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -2981,11 +3086,11 @@ hbox{$
 Lang{reach}$}}}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -3000,11 +3105,11 @@ Lang{approx}_{
 operatorname{tourn}}$''}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3030,15 +3135,17 @@ The Circuit Complexity Classes AC
 \end_inset
 
 
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Limit the Circuit Depth
 \end_layout
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3047,11 +3154,11 @@ setlength
 leftmargini{1em}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3067,7 +3174,7 @@ nointerlineskip
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [t]
 \end_layout
@@ -3086,7 +3193,7 @@ status collapsed
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \end_layout
@@ -3101,7 +3208,7 @@ Circuit Class
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -3156,7 +3263,7 @@ unbounded fan-in
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \end_layout
@@ -3171,7 +3278,7 @@ Circuit Class
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -3233,7 +3340,7 @@ bounded fan-in
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \end_layout
@@ -3248,7 +3355,7 @@ Circuit Class
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -3289,7 +3396,7 @@ bounded fan-in
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <2>
 \end_layout
@@ -3305,7 +3412,9 @@ Standard Complexity Results on Finding Paths
 
 \begin_layout BeginFrame
 All Variants of Finding Paths in Directed Graphs
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Are Equally Difficult
 \end_layout
 
@@ -3371,7 +3480,7 @@ the approximation problem in logspace iff
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <3>
 \end_layout
@@ -3383,7 +3492,9 @@ hierarchy
 
 \begin_layout BeginFrame
 FindingPaths in Forests and Directed Paths is Easy,
-\newline
+\begin_inset Newline newline
+\end_inset
+
 But Not Trivial
 \end_layout
 
@@ -3425,7 +3536,7 @@ But Not Trivial
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <4>
 \end_layout
@@ -3448,15 +3559,19 @@ Definition of the Tournament Reachability Problem
 \end_layout
 
 \begin_layout Definition
-Let 
+Let
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Lang{reach}_{\operatorname{tourn}}$
 \end_inset
 
 
+\color none
+ 
 \color inherit
- contain all triples 
+contain all triples 
 \begin_inset Formula $(T,s,t)$
 \end_inset
 
@@ -3472,12 +3587,18 @@ Let
 \end_layout
 
 \begin_layout Enumerate
-there exists a path from\InsetSpace ~
+there exists a path from
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -3503,9 +3624,9 @@ The Tournament Reachability Problem is Very Easy
 
 \begin_layout AlertBlock
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Implications}
 \end_layout
@@ -3548,7 +3669,7 @@ easier
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <5>
 \end_layout
@@ -3564,17 +3685,23 @@ Complexity of: Construct a Shortest Path
 
 \begin_layout BeginFrame
 Finding a Shortest Path Is as Difficult as
-\newline
+\begin_inset Newline newline
+\end_inset
+
 the Distance Problem
 \end_layout
 
 \begin_layout Definition
-Let 
+Let
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
 
+
+\color none
  
 \color inherit
 contain all tuples 
@@ -3597,12 +3724,18 @@ 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
@@ -3627,13 +3760,14 @@ 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
@@ -3653,9 +3787,10 @@ 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
 
@@ -3685,7 +3820,7 @@ Proof That
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3699,9 +3834,9 @@ nointerlineskip
 
 \begin_layout Columns
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [t,onlytextwidth]
 \end_layout
@@ -3718,9 +3853,9 @@ status inlined
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -3738,7 +3873,7 @@ leftmargini{1.5em}
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \end_layout
@@ -3757,7 +3892,7 @@ Reduce
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -3770,9 +3905,9 @@ status collapsed
 \begin_deeper
 \begin_layout Enumerate
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <alert@1>
 \end_layout
@@ -3792,9 +3927,9 @@ Is input
 
 \begin_layout Enumerate
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <2-| alert@2-8>
 \end_layout
@@ -3814,9 +3949,9 @@ Map
 
 \begin_layout Enumerate
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <9-| alert@9>
 \end_layout
@@ -3824,7 +3959,9 @@ status inlined
 \end_inset
 
 Query:
-\newline
+\begin_inset Newline newline
+\end_inset
+
 
 \begin_inset Formula $(G',s',t',3)\in\Lang{distance}_{\operatorname{tourn}}$
 \end_inset
@@ -3841,7 +3978,7 @@ Query:
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {
 \end_layout
@@ -3852,7 +3989,7 @@ Correctness
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 }
 \end_layout
@@ -3863,7 +4000,7 @@ status collapsed
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <10->
 \end_layout
@@ -3876,23 +4013,31 @@ status collapsed
 \begin_deeper
 \begin_layout Enumerate
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\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
@@ -3902,23 +4047,31 @@ a length-3 path in\InsetSpace ~
 
 \begin_layout Enumerate
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\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
@@ -3933,42 +4086,42 @@ 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
+\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
@@ -3977,11 +4130,11 @@ graphnode{A}{
 pgfxy(1,3.3)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -3990,11 +4143,11 @@ graphnode{B}{
 pgfxy(2,3.3)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4003,11 +4156,11 @@ graphnode{C}{
 pgfxy(3,3.3)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4016,30 +4169,30 @@ graphnode{D}{
 pgfxy(4,3.3)}
 \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
@@ -4050,11 +4203,11 @@ pgfnodecenter{A}}{
 pgfbox[center,center]{$s$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4065,30 +4218,30 @@ pgfnodecenter{D}}{
 pgfbox[center,center]{$t$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \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
@@ -4097,33 +4250,33 @@ 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{2pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4132,11 +4285,11 @@ alert<3>{
 pgfnodeconnline{B}{A}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4145,11 +4298,11 @@ alert<4>{
 pgfnodeconnline{B}{C}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4158,11 +4311,11 @@ alert<5,10-11,13>{
 pgfnodeconnline{C}{D}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
@@ -4171,20 +4324,20 @@ alert<6,10-11,13>{
 pgfnodeconncurve{A}{C}{45}{135}{15pt}{15pt}}
 \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
@@ -4197,30 +4350,30 @@ pgfbox[left,center]{$G
 colon$}}
 \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
 only<2->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4233,11 +4386,11 @@ pgfbox[left,center]{$G'
 colon$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4246,11 +4399,11 @@ graphnode{A1}{
 pgfxy(1,2.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4259,11 +4412,11 @@ graphnode{B1}{
 pgfxy(2,2.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4272,11 +4425,11 @@ graphnode{C1}{
 pgfxy(3,2.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4285,19 +4438,19 @@ graphnode{D1}{
 pgfxy(4,2.25)}
 \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
@@ -4306,11 +4459,11 @@ graphnode{A2}{
 pgfxy(1,1.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4319,11 +4472,11 @@ graphnode{B2}{
 pgfxy(2,1.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4332,11 +4485,11 @@ graphnode{C2}{
 pgfxy(3,1.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4345,11 +4498,11 @@ graphnode{D2}{
 pgfxy(4,1.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4358,11 +4511,11 @@ graphnode{A3}{
 pgfxy(1,0.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4371,11 +4524,11 @@ graphnode{B3}{
 pgfxy(2,0.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4384,11 +4537,11 @@ graphnode{C3}{
 pgfxy(3,0.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4397,11 +4550,11 @@ graphnode{D3}{
 pgfxy(4,0.25)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4410,11 +4563,11 @@ graphnode{A4}{
 pgfxy(1,-.75)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4423,11 +4576,11 @@ graphnode{B4}{
 pgfxy(2,-.75)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4436,11 +4589,11 @@ graphnode{C4}{
 pgfxy(3,-.75)}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -4449,22 +4602,22 @@ graphnode{D4}{
 pgfxy(4,-.75)}
 \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
@@ -4475,11 +4628,11 @@ pgfnodecenter{A1}}{
 pgfbox[center,center]{$s'$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
       
 \backslash
@@ -4490,334 +4643,334 @@ pgfnodecenter{D4}}{
 pgfbox[center,center]{$t'$}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   }}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
    
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<8->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfsetlinewidth{0.4pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color{beamerexample!25!averagebackgroundcolor}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A2}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{A1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C2}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D2}{A1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D2}{B1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A3}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{A2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C3}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D3}{A2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D3}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A4}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B4}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B4}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C4}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D4}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D4}{B3}
 \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
@@ -4826,511 +4979,511 @@ pgfsetstartarrow{
 pgfarrowto}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A1}{B1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B1}{C1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C1}{D1}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A2}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C2}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A3}{B3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C3}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A4}{B4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B4}{C4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C4}{D4}
 \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
 pgfclearstartarrow
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{A3}{A1}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{A4}{A2}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{A4}{A1}{135}{-135}{15pt}{15pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
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 pgfnodeconncurve{B3}{B1}{135}{-135}{10pt}{10pt}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
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-\begin_layout Standard
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-\begin_layout Standard
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-\begin_layout Standard
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-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{C3}{C1}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{C4}{C2}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{C4}{C1}{135}{-135}{15pt}{15pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{D3}{D1}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{D4}{D2}{135}{-135}{10pt}{10pt}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconncurve{D4}{D1}{135}{-135}{15pt}{15pt}
 \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
 
   }
 \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
 only<3->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color<3>{red}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B1}{A2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{A4}
 \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
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<4->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color<4>{red}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B1}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{C4}
 \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
 
   
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<5->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color<5>{red}
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-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C1}{D2} 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5339,11 +5492,11 @@ alert<11>{
 pgfnodeconnline{C2}{D3}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5352,51 +5505,51 @@ alert<12-13>{
 pgfnodeconnline{C3}{D4}}
 \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
 
  
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<6->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color<6>{red}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5405,11 +5558,11 @@ alert<11>{
 pgfnodeconnline{A1}{C2}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5418,61 +5571,61 @@ alert<12-13>{
 pgfnodeconnline{A2}{C3}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A3}{C4}
 \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
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
   
 \backslash
 only<7->{
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 color<7>{red}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5481,121 +5634,121 @@ alert<12-13>{
 pgfnodeconnline{A1}{A2}}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A2}{A3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{A3}{A4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B1}{B2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B2}{B3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{B3}{B4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C1}{C2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C2}{C3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{C3}{C4}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D1}{D2}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
 pgfnodeconnline{D2}{D3}
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
     
 \backslash
@@ -5604,20 +5757,20 @@ alert<11>{
 pgfnodeconnline{D3}{D4}}
 \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
@@ -5634,7 +5787,7 @@ end{pgfpicture}
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <6>
 \end_layout
@@ -5653,15 +5806,19 @@ Approximators Compute Paths that Are Nearly As Short As a Shortest Path
 \end_layout
 
 \begin_layout Definition
-An 
+An
+\color none
+ 
 \color red
 approximation scheme for 
 \begin_inset Formula $\Lang{tournament-shortest-path}$
 \end_inset
 
 
+\color none
+ 
 \color inherit
- gets as input
+gets as input
 \end_layout
 
 \begin_deeper
@@ -5690,7 +5847,10 @@ a path from
 \begin_inset Formula $s$
 \end_inset
 
- to\InsetSpace ~
+ to
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $t$
 \end_inset
@@ -5705,9 +5865,10 @@ a path from
 \end_deeper
 \begin_layout BeginFrame
 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
 
 \begin_layout Theorem
@@ -5720,8 +5881,10 @@ 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
 
@@ -5737,13 +5900,14 @@ In tournaments, paths can be constructed in logarithmic space.
 \end_layout
 
 \begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
 
-\hfill
 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5761,7 +5925,7 @@ beamergotobutton{More Details}}
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <7>
 \end_layout
@@ -5771,6 +5935,158 @@ status collapsed
 hierarchy
 \end_layout
 
+\begin_layout EndFrame
+
+\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
+
+.
+ This is not yet supported by LyX, so the frame is created using TeX code.
+ Note that the 
+\backslash
+begin{frame}[fragile] needs to be preceeded by an 
+\emph on
+EndFrame
+\emph default
+ environment.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{frame}[fragile]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+frametitle{
+\end_layout
+
+\end_inset
+
+Just a frame with a program code listing
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This is some program code:
+\end_layout
+
+\begin_layout Standard
+\begin_inset listings
+lstparams "extendedchars=true,language=Python,numbers=left,stepnumber=3,tabsize=4"
+inline false
+status open
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+    'this is a python function'
+\end_layout
+
+\begin_layout Plain Layout
+
+    pass
+\end_layout
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+'This is a German word: Tschüs'
+\end_layout
+
+\begin_layout Plain Layout
+
+pass
+\end_layout
+
+\begin_layout Plain Layout
+
+def func(param):
+\end_layout
+
+\begin_layout Plain Layout
+
+'this is a python function'
+\end_layout
+
+\begin_layout Plain Layout
+
+pass
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{frame}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section*
 Summary
 \end_layout
@@ -5785,9 +6101,9 @@ Summary
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Summary}
 \end_layout
@@ -5799,13 +6115,19 @@ status inlined
 
 \begin_deeper
 \begin_layout Itemize
-Tournament 
+Tournament
+\color none
+ 
 \color red
 reachability
+\color none
+ 
 \color inherit
- is in
-\color red
+is in
+\color none
  
+\color red
+
 \begin_inset Formula $\Class{AC}^{0}$
 \end_inset
 
@@ -5816,25 +6138,39 @@ reachability
 \end_layout
 
 \begin_layout Itemize
-There exists a 
+There exists a
+\color none
+ 
 \color red
 logspace approximation scheme
+\color none
+ 
 \color inherit
- for 
+for
+\color none
+ 
 \color red
 approximating
+\color none
+ 
 \color inherit
- shortest paths in tournaments.
+shortest paths in tournaments.
 \end_layout
 
 \begin_layout Itemize
-Finding 
+Finding
+\color none
+ 
 \color red
 shortest paths
+\color none
+ 
 \color inherit
- in tournaments is
-\color red
+in tournaments is
+\color none
  
+\color red
+
 \begin_inset Formula $\Class{NL}$
 \end_inset
 
@@ -5850,9 +6186,9 @@ shortest paths
 
 \begin_layout Block
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 {Outlook}
 \end_layout
@@ -5865,14 +6201,18 @@ 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
@@ -5888,14 +6228,18 @@ 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
@@ -5920,9 +6264,9 @@ For Further Reading
 
 \begin_layout Standard
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5935,15 +6279,23 @@ beamertemplatebookbibitems
 \end_layout
 
 \begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Moon1968"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {Moon1968}
-\InsetSpace ~
 John Moon.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5961,7 +6313,7 @@ Topics on Tournaments.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5973,9 +6325,9 @@ newblock
  Holt, Rinehart, and Winston, 1968.
  
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -5988,15 +6340,23 @@ beamertemplatearticlebibitems
 \end_layout
 
 \begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "NickelsenT2002"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {NickelsenT2002}
-\InsetSpace ~
 Arfst Nickelsen and Till Tantau.
  
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6009,7 +6369,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6027,14 +6387,22 @@ Proc.
 \end_layout
 
 \begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Tantau2004b"
+
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
 
-\bibitem {Tantau2004b}
-\InsetSpace ~
 Till Tantau 
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6048,7 +6416,7 @@ newblock
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6067,7 +6435,7 @@ Proc.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6086,9 +6454,9 @@ newblock
 \begin_layout Standard
 \start_of_appendix
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6110,9 +6478,9 @@ Graphs With Bounded Independence Number
 
 \begin_layout BeginFrame
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [label=independence]
 \end_layout
@@ -6123,20 +6491,27 @@ Definition of Independence Number of a Graph
 \end_layout
 
 \begin_layout Definition
-The 
+The
+\color none
+ 
 \color red
 independence number
-\color inherit
+\color none
  
+\color inherit
+
 \begin_inset Formula $\alpha(G)$
 \end_inset
 
  of a directed graph
-\newline
+\begin_inset Newline newline
+\end_inset
+
 is the maximum number of vertices we can pick,
-\newline
-such that
- there is no edge between them.
+\begin_inset Newline newline
+\end_inset
+
+such that there is no edge between them.
 \end_layout
 
 \begin_layout Example
@@ -6146,24 +6521,37 @@ Tournaments have independence number 1.
 
 \begin_layout BeginFrame
 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
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, 
+,
+\color none
+ 
 \color red
 reachability
+\color none
+ 
 \color inherit
- in graphs with independence number
-\newline
-at most\InsetSpace ~
+in graphs with independence number
+\begin_inset Newline newline
+\end_inset
+
+at most
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
@@ -6180,17 +6568,27 @@ at most\InsetSpace ~
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, there exists a 
+, there exists a
+\color none
+ 
 \color red
 logspace approximation scheme
+\color 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
@@ -6203,21 +6601,33 @@ logspace approximation scheme
 \end_layout
 
 \begin_layout Theorem
-For each\InsetSpace ~
+For each
+\begin_inset space ~
+\end_inset
+
 
 \begin_inset Formula $k$
 \end_inset
 
-, finding the 
+, finding the
+\color none
+ 
 \color red
 shortest path
+\color 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
 
- is 
+ is
+\color none
+ 
 \color red
 
 \begin_inset Formula $\Class{NL}$
@@ -6234,9 +6644,9 @@ Finding Paths in Undirected Graphs
 
 \begin_layout BeginFrame
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 <1-2>[label=undirected]
 \end_layout
@@ -6244,7 +6654,9 @@ status inlined
 \end_inset
 
 The Complexity of Finding Paths in Undirected Graphs
-\newline
+\begin_inset Newline newline
+\end_inset
+
 Is Party Unknown.
 \end_layout
 
@@ -6275,9 +6687,9 @@ the reachability problem in logspace iff
 \begin_layout Itemize
 the construction problem in logspace iff 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6298,9 +6710,9 @@ Class{SL}$}}
 \begin_layout Itemize
 the optimization problem in logspace iff 
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash
@@ -6330,9 +6742,9 @@ The Approximation Scheme is Optimal
 
 \begin_layout BeginFrame
 \begin_inset ERT
-status inlined
+status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 [label=optimality]
 \end_layout
@@ -6366,7 +6778,9 @@ 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
@@ -6394,7 +6808,9 @@ 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
@@ -6408,7 +6824,7 @@ The resulting path has optimal length.
 \begin_inset ERT
 status collapsed
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 
 \backslash