UserGuide.lyx: fix some typographic issues spotted by Mike

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

diff --git a/lib/examples/beamerlyxexample1.lyx b/lib/examples/beamerlyxexample1.lyx
index 8464a2d70c7d0f9fa897c9f4ee61e97890d60a50..9d51a378bcbba090a36eeb2befa4b16c9d367482 100644 (file)
--- a/lib/examples/beamerlyxexample1.lyx
+++ b/lib/examples/beamerlyxexample1.lyx
@@ -1,7 +1,9 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 459
+#LyX 2.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 508
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
 \textclass beamer
 \begin_preamble
 \beamertemplateshadingbackground{red!5}{structure!5}
@@ -155,16 +157,16 @@
 \language_package default
 \inputencoding auto
 \fontencoding global
-\font_roman times
-\font_sans default
-\font_typewriter default
-\font_math auto
+\font_roman "times" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "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
 \graphics default
 \default_output_format default
 \output_sync 0
@@ -177,6 +179,7 @@
 \use_geometry false
 \use_package amsmath 2
 \use_package amssymb 2
+\use_package cancel 0
 \use_package esint 0
 \use_package mathdots 1
 \use_package mathtools 0
@@ -185,7 +188,7 @@
 \use_package stmaryrd 0
 \use_package undertilde 0
 \cite_engine basic
-\cite_engine_type numerical
+\cite_engine_type default
 \biblio_style plain
 \use_bibtopic false
 \use_indices false
@@ -248,10 +251,20 @@ 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
@@ -272,13 +285,10 @@ 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
 
@@ -341,10 +351,20 @@ 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
@@ -579,10 +599,28 @@ 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
@@ -828,20 +866,38 @@ 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 Argument 2
 status collapsed
@@ -866,7 +922,10 @@ 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
 
@@ -894,7 +953,10 @@ 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
 
@@ -932,15 +994,26 @@ It chooses from any two words the one more likely to be in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection
 What Does ``Finding Paths'' Mean?
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 ``Finding Paths'' is Ambiguous
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status open
@@ -2096,6 +2169,7 @@ Problem: Construct a path from
 approximately their distance.
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout Section
@@ -2125,7 +2199,11 @@ 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
@@ -2133,6 +2211,12 @@ 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 collapsed
@@ -2296,10 +2380,28 @@ 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
 Logspace Turing Machines Are Quite Powerful
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status collapsed
@@ -2358,20 +2460,48 @@ satisfiability with two literals per clause.
 \end_layout
 
 \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 1
 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
@@ -2755,7 +2885,19 @@ 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
@@ -2775,6 +2917,12 @@ 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
@@ -2983,6 +3131,7 @@ bounded fan-in
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \end_deeper
 \begin_layout AgainFrame
@@ -3002,7 +3151,11 @@ 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
@@ -3010,6 +3163,12 @@ 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
@@ -3067,6 +3226,7 @@ the approximation problem in logspace iff
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -3081,7 +3241,11 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout BeginFrame
+\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
@@ -3089,6 +3253,12 @@ Finding Paths in Forests and Directed Paths is Easy,
 But Not Trivial
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Fact
 \begin_inset Formula $\Lang{reach}_{\operatorname{forest}}$
 \end_inset
@@ -3104,7 +3274,10 @@ But Not Trivial
 -complete.
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -3123,6 +3296,7 @@ But Not Trivial
 -complete.
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
 status collapsed
@@ -3144,10 +3318,20 @@ 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
@@ -3197,10 +3381,28 @@ 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
@@ -3253,6 +3455,7 @@ easier
 .
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -3271,7 +3474,11 @@ 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
@@ -3279,6 +3486,12 @@ 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
@@ -3332,10 +3545,28 @@ 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
@@ -3396,7 +3627,19 @@ 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
@@ -3404,6 +3647,12 @@ Proof That
  is NL-complete
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status collapsed
@@ -3542,7 +3791,10 @@ Query:
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -4692,6 +4944,7 @@ end{pgfpicture}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
@@ -4710,10 +4963,20 @@ 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
@@ -4772,7 +5035,19 @@ 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
@@ -4780,6 +5055,12 @@ 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 $\Lang{tournament-shortest-path}$
@@ -4830,6 +5111,7 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \begin_layout AgainFrame
 \begin_inset Argument 1
 status collapsed
@@ -4843,10 +5125,6 @@ status collapsed
 hierarchy
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
 \begin_layout Standard
 \begin_inset Note Note
 status open
@@ -4861,7 +5139,8 @@ fragile
 \end_inset
 
 .
- LyX has the FragileFrame layout for this.
+ \SpecialChar LyX
+ has the FragileFrame layout for this.
 \end_layout
 
 \end_inset
@@ -4952,10 +5231,20 @@ Summary
 Summary
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 Summary
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Block
 \begin_inset Argument 2
 status collapsed
@@ -5036,7 +5325,10 @@ in tournaments is
 \end_layout
 
 \end_deeper
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -5108,15 +5400,26 @@ beamergotobutton{More Details}}
 
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsection*
 For Further Reading
 \end_layout
 
-\begin_layout BeginFrame
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
 For Further Reading
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
 \begin_layout Standard
 \begin_inset ERT
 status open
@@ -5299,10 +5602,7 @@ newblock
  In press.
 \end_layout
 
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \begin_layout Standard
 \start_of_appendix
 \begin_inset ERT
@@ -5328,20 +5628,30 @@ 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
@@ -5371,7 +5681,19 @@ 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
@@ -5379,6 +5701,12 @@ 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 ~
@@ -5415,7 +5743,10 @@ at most
 .
 \end_layout
 
-\begin_layout Separator
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
 
 \end_layout
 
@@ -5448,7 +5779,10 @@ 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
 
@@ -5490,21 +5824,36 @@ 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
@@ -5512,6 +5861,12 @@ 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
@@ -5633,25 +5988,36 @@ 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 $\Lang{tournament-shortest-path}$
@@ -5735,9 +6101,6 @@ qedhere
 \end_layout
 
 \end_deeper
-\begin_layout EndFrame
-
-\end_layout
-
+\end_deeper
 \end_body
 \end_document