summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex')
-rw-r--r--Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex941
1 files changed, 941 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex b/Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex
new file mode 100644
index 00000000000..eaa7e9b642c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/beamer/examples/beamerexample1.tex
@@ -0,0 +1,941 @@
+% $Header: /cvsroot/latex-beamer/latex-beamer/examples/beamerexample1.tex,v 1.47 2004/11/04 15:43:51 tantau Exp $
+
+\documentclass{beamer}
+%\documentclass{article}
+%\usepackage[envcountsect]{beamerarticle}
+
+% Do NOT take this file as a template for your own talks. Use a file
+% in the directory solutions instead. They are much better suited.
+
+% Try the class options [notes], [notes=only], [trans], [handout],
+% [red], [compress], [draft] and see what happens!
+
+% Copyright 2003 by Till Tantau <tantau@users.sourceforge.net>.
+%
+% This program can be redistributed and/or modified under the terms
+% of the LaTeX Project Public License Distributed from CTAN
+% archives in directory macros/latex/base/lppl.txt.
+
+% For a green structure color use:
+%\colorlet{structure}{green!50!black}
+
+\mode<article> % only for the article version
+{
+ \usepackage{fullpage}
+ \usepackage{hyperref}
+}
+
+
+\mode<presentation>
+{
+ \setbeamertemplate{background canvas}[vertical shading][bottom=red!10,top=blue!10]
+
+ \usetheme{Warsaw}
+ \usefonttheme[onlysmall]{structurebold}
+}
+
+%\setbeamercolor{math text}{fg=green!50!black}
+%\setbeamercolor{normal text in math text}{parent=math text}
+
+\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
+\usepackage{amsmath,amssymb}
+\usepackage[latin1]{inputenc}
+\usepackage{colortbl}
+\usepackage[english]{babel}
+
+%\usepackage{lmodern}
+%\usepackage[T1]{fontenc}
+
+\usepackage{times}
+
+\setbeamercovered{dynamic}
+
+%
+% The following defintions are peculiar to this particular
+% presetation. They have nothing to do with the beamer class
+%
+
+\newcommand{\Lang}[1]{\operatorname{\text{\textsc{#1}}}}
+
+\newcommand{\Class}[1]{\operatorname{\mathchoice
+ {\text{\normalfont\small #1}}
+ {\text{\normalfont\small #1}}
+ {\text{\normalfont#1}}
+ {\text{\normalfont#1}}}}
+
+\newcommand{\DOF}{\Class{DOF}}
+\newcommand{\NOF}{\Class{NOF}}
+\newcommand{\DOFpoly}{\Class{DOF}_{\operatorname{poly}}}
+\newcommand{\NOFpoly}{\Class{NOF}_{\operatorname{poly}}}
+
+
+\newcommand{\Nat}{\mathbb{N}}
+\newcommand{\Set}[1]{\{#1\}}
+
+\pgfdeclaremask{computer}{beamer-computer-mask}
+\pgfdeclaremask{apple}{beamer-g4-mask}
+\pgfdeclaremask{ram}{beamer-ram-mask}
+
+\pgfdeclareimage[interpolate=true,mask=computer,%
+ width=1.8361cm,height=2cm]{computerimage}{beamer-computer}
+\pgfdeclareimage[interpolate=true,mask=computer,%
+ width=1.8361cm,height=2cm]{computerworkingimage}{beamer-computerred}
+\pgfdeclareimage[interpolate=true,mask=apple,%
+ width=1.625cm,height=2cm]{apple}{beamer-g4}
+\pgfdeclareimage[interpolate=true,mask=apple,%
+ width=1.625cm,height=2cm]{appleworking}{beamer-g4red}
+\pgfdeclareimage[interpolate=true,mask=ram,%
+ width=3.811cm,height=1cm]{ram}{beamer-ram}
+
+\newcommand{\tape}[9]{%
+ \pgfputat{#1}{%
+ \pgfsetlinewidth{0.8pt}%
+ \pgfrect[stroke]{\pgfxy(0,0)}{\pgfxy(4,0.5)}%
+ \pgfsetlinewidth{0.4pt}%
+ \pgfline{\pgfxy(0.5,0)}{\pgfxy(0.5,0.5)}%
+ \pgfline{\pgfxy(1.0,0)}{\pgfxy(1.0,0.5)}%
+ \pgfline{\pgfxy(1.5,0)}{\pgfxy(1.5,0.5)}%
+ \pgfline{\pgfxy(2.0,0)}{\pgfxy(2.0,0.5)}%
+ \pgfline{\pgfxy(2.5,0)}{\pgfxy(2.5,0.5)}%
+ \pgfline{\pgfxy(3.0,0)}{\pgfxy(3.0,0.5)}%
+ \pgfline{\pgfxy(3.5,0)}{\pgfxy(3.5,0.5)}%
+ %
+ \pgfputat{\pgfxy(0.25,0.25)}{\pgfbox[center,center]{#2}}%
+ \pgfputat{\pgfxy(0.75,0.25)}{\pgfbox[center,center]{#3}}%
+ \pgfputat{\pgfxy(1.25,0.25)}{\pgfbox[center,center]{#4}}%
+ \pgfputat{\pgfxy(1.75,0.25)}{\pgfbox[center,center]{#5}}%
+ \pgfputat{\pgfxy(2.25,0.25)}{\pgfbox[center,center]{#6}}%
+ \pgfputat{\pgfxy(2.75,0.25)}{\pgfbox[center,center]{#7}}%
+ \pgfputat{\pgfxy(3.25,0.25)}{\pgfbox[center,center]{#8}}%
+ \pgfputat{\pgfxy(3.75,0.25)}{\pgfbox[center,center]{#9}}%
+ %
+ \pgfputat{\pgfxy(0,0.7)}{\pgfbox[left,base]{\structure{tape}}}%
+ }%
+ %
+ \pgfnodecircle{n1}[virtual]{\pgfrelative{#1}{\pgfxy(0.25,0)}}{2pt}%
+ \pgfnodecircle{n2}[virtual]{\pgfrelative{#1}{\pgfxy(0.75,0)}}{2pt}%
+ \pgfnodecircle{n3}[virtual]{\pgfrelative{#1}{\pgfxy(1.25,0)}}{2pt}%
+ \pgfnodecircle{n4}[virtual]{\pgfrelative{#1}{\pgfxy(1.75,0)}}{2pt}%
+ \pgfnodecircle{n5}[virtual]{\pgfrelative{#1}{\pgfxy(2.25,0)}}{2pt}%
+ \pgfnodecircle{n6}[virtual]{\pgfrelative{#1}{\pgfxy(2.75,0)}}{2pt}%
+ \pgfnodecircle{n7}[virtual]{\pgfrelative{#1}{\pgfxy(3.25,0)}}{2pt}%
+ \pgfnodecircle{n8}[virtual]{\pgfrelative{#1}{\pgfxy(3.75,0)}}{2pt}%
+}
+
+\newcommand{\putmachine}[2]{%
+ \pgfputat{#1}{\pgfbox[center,center]{\pgfuseimage{computerimage}}}%
+ \pgfputat{\pgfrelative{#1}{\pgfxy(0,-1.4)}}{\pgfbox[center,base]{\structure{#2}}}%
+ \pgfnodecircle{machine}[virtual]{\pgfrelative{#1}{\pgfxy(0,1)}}{2pt}%
+}
+\newcommand{\putmachineworking}[2]{%
+ \pgfputat{#1}{\pgfbox[center,center]{\pgfuseimage{computerworkingimage}}}%
+ \pgfputat{\pgfrelative{#1}{\pgfxy(0,-1.4)}}{\pgfbox[center,base]{\structure{#2}}}%
+ \pgfnodecircle{machine}[virtual]{\pgfrelative{#1}{\pgfxy(0,1)}}{2pt}%
+}
+
+\newcommand{\putmachinea}[2]{%
+ \pgfputat{#1}{\pgfbox[center,center]{\pgfuseimage{apple}}}%
+ \pgfputat{\pgfrelative{#1}{\pgfxy(0,-1.4)}}{\pgfbox[center,base]{\structure{#2}}}%
+ \pgfnodecircle{machine}[virtual]{\pgfrelative{#1}{\pgfxy(0,1)}}{2pt}%
+}
+\newcommand{\putmachineworkinga}[2]{%
+ \pgfputat{#1}{\pgfbox[center,center]{\pgfuseimage{appleworking}}}%
+ \pgfputat{\pgfrelative{#1}{\pgfxy(0,-1.4)}}{\pgfbox[center,base]{\structure{#2}}}%
+ \pgfnodecircle{machine}[virtual]{\pgfrelative{#1}{\pgfxy(0,1)}}{2pt}%
+}
+
+\newcommand{\selectpos}[1]{%
+ \pgfsetlinewidth{0.6pt}%
+ \color{structure}%
+ \pgfsetendarrow{\pgfarrowto}%
+ \pgfnodeconncurve{machine}{n#1}{90}{-90}{.5cm}{.5cm}%
+}
+
+%
+% The following info should normally be given in you main file:
+%
+
+\title[Computation with Absolutely No~Space~Overhead]{Computation~with Absolutely~No~Space~Overhead}
+\author[Hemaspaandra, Mukherji, Tantau]{%
+ Lane~Hemaspaandra\inst{1} \and
+ Proshanto~Mukherji\inst{1} \and
+ Till~Tantau\inst{2}}
+\institute[Universities of Rochester and Berlin]{
+ \inst{1}%
+ Department of Computer Science\\
+ University of Rochester
+ \and
+ \inst{2}%
+ Fakultät für Elektrotechnik und Informatik\\
+ Technical University of Berlin}
+\date[DLT 2003]{Developments in Language Theory Conference, 2003}
+\subject{Theoretical Computer Science}
+
+\pgfdeclaremask{tu}{beamer-tu-logo-mask}
+\pgfdeclaremask{ur}{beamer-ur-logo-mask}
+\pgfdeclareimage[mask=tu,width=0.6cm]{tu-logo}{beamer-tu-logo}
+\pgfdeclareimage[mask=ur,width=1cm]{ur-logo}{beamer-ur-logo}
+
+\logo{\vbox{\hbox to 1cm{\hfil\pgfuseimage{tu-logo}}\vskip0.1cm\hbox{\pgfuseimage{ur-logo}}}}
+
+
+\begin{document}
+
+\frame{\titlepage}
+
+\section<presentation>*{Outline}
+
+\begin{frame}
+ \frametitle{Outline}
+ \tableofcontents[part=1,pausesections]
+\end{frame}
+
+\AtBeginSubsection[]
+{
+ \begin{frame}<beamer>
+ \frametitle{Outline}
+ \tableofcontents[current,currentsubsection]
+ \end{frame}
+}
+
+\part<presentation>{Main Talk}
+
+\section[Models]{The Model of Overhead-Free Computation}
+
+\subsection[Standard Model]{The Standard Model of Linear Space}
+
+\begin{frame}
+ \frametitle{The Standard Model of Linear Space}
+
+ \begin{columns}
+
+ \column{4.5cm}
+ \note[item]<1>{Point out that \$ is a marker symbol.}
+ \begin{pgfpicture}{-0.5cm}{1cm}{4cm}{7cm}
+ \only<1| trans:1>{
+ \putmachine{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{1}}
+ \only<2| handout:0| trans:2>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{2}}
+ \only<3| handout:0| trans:3>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{8}}
+ \only<4| handout:0| trans:4>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{0}{1}{0}{0}{1}{0}{\$}
+ \selectpos{7}}
+ \only<5| handout:0| trans:0>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{0}{1}{0}{0}{1}{0}{\$}
+ \selectpos{2}}
+ \only<6| handout:0| trans:0>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{\$}{1}{0}{0}{1}{0}{\$}
+ \selectpos{3}}
+ \only<7| handout:0| trans:0>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{\$}{1}{0}{0}{1}{0}{\$}
+ \selectpos{7}}
+ \only<8| handout:0| trans:0>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{\$}{1}{0}{0}{1}{\$}{\$}
+ \selectpos{6}}
+ \only<9| handout:0| trans:0>{
+ \putmachineworking{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{\$}{\$}{\$}{\$}{\$}{\$}{\$}
+ \selectpos{5}}
+ \only<10| handout:0| trans:5>{
+ \putmachine{\pgfxy(1.75,3)}{Turing machine}
+ \tape{\pgfxy(0,5)}{\$}{\$}{\$}{\$}{\$}{\$}{\$}{\$}
+ \selectpos{5}}
+ \end{pgfpicture}
+
+ \column{6cm}
+ \begin{block}{Characteristics}
+ \begin{itemize}
+ \item
+ Input fills \alert{fixed-size tape}
+ \item
+ Input may be \alert{modified}
+ \item
+ Tape alphabet \alert{is larger than}\\ input alphabet
+ \note[item]<1>{Stress the larger tape alphabet.}
+ \end{itemize}
+ \end{block}
+ \end{columns}
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{Linear Space is a Powerful Model}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{6cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{2cm}{2.5cm}{$\Class{CFL}$}
+ \pgfheaplabeledcentered{3.5cm}{3cm}{\raise10pt\hbox{}$\Class{DLINSPACE}$}
+ \pgfheaplabeledcentered{5cm}{4cm}{\raise13pt\hbox{}$\Class{NLINSPACE} = \Class{CSL}$}
+ \pgfheaplabeledcentered{6cm}{5cm}{$\Class{PSPACE}$}
+ \note[item]{Explain CSL.}
+
+ \pgfsetdash{{3pt}{3pt}}{0pt}
+ \pgfheaplabeled{\pgfxy(0,3.3)}{\pgfxy(-5,6)}{\pgfxy(5,6)}{}%
+ \pgfputat{\pgfxy(-4.6,5.75)}{\pgfbox[left,base]{$\Class{PSPACE}\!\text{-hard}$}}%
+ \end{pgfpicture}
+ \note[item]{Point out the connections to formal language theory.}
+\end{frame}
+
+
+\subsection[Our Model]{Our Model of Absolutely No Space Overhead}
+
+\begin{frame}
+ \frametitle{Our Model of ``Absolutely No Space Overhead''}
+
+ \transdissolve<7>[duration=0.2]
+
+ \begin{columns}
+
+ \column{4.5cm}
+ \begin{pgfpicture}{-0.5cm}{1cm}{4cm}{7cm}
+ \only<1| trans:1>{%
+ \putmachinea{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{0}{0}%
+ \selectpos{1}}%
+ \only<2| handout:0| trans:2>{%
+ \putmachineworkinga{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{0}%
+ \selectpos{2}}%
+ \only<3| handout:0| trans:3>{%
+ \putmachineworkinga{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{0}%
+ \selectpos{8}}%
+ \only<4| handout:0| trans:0>{%
+ \putmachineworkinga{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{1}%
+ \selectpos{7}}%
+ \only<5| handout:0| trans:0>{%
+ \putmachineworkinga{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{1}%
+ \selectpos{2}}%
+ \only<6| handout:0| trans:0>{%
+ \putmachineworkinga{\pgfxy(1.75,3)}{Turing machine}%
+ \tape{\pgfxy(0,5)}{1}{1}{1}{0}{0}{1}{0}{1}%
+ \selectpos{3}}%
+ \only<7| handout:0| trans:4>{%
+ \putmachinea{\pgfxy(1.75,3)}{Turing machine}%
+ \pgfputat{\pgfxy(1.75,5.5)}{\pgfbox[center,center]{\pgfuseimage{ram}}}%
+ \pgfnodecircle{n3}[virtual]{\pgfxy(1.25,5)}{2pt}%
+ \selectpos{3}}%
+ \end{pgfpicture}
+
+ \column{6cm}
+ \begin{overprint}
+ \onslide<1-6| trans:1-3| handout:1>
+ \begin{block}{Characteristics}
+ \begin{itemize}
+ \item
+ Input fills \alert{fixed-size tape}
+ \item
+ Input may be \alert{modified}
+ \item
+ Tape alphabet \alert{equals}\\
+ input alphabet
+ \end{itemize}
+ \end{block}
+ \onslide<7-| trans:4| handout:2>
+ \begin{alertblock}{Intuition}
+ \begin{itemize}
+ \item
+ Tape is used like a\\ RAM module.
+ \end{itemize}
+ \end{alertblock}
+ \end{overprint}
+ \end{columns}
+ \note[item]<6>{Point out that no markers are used.}
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{Definition of Overhead-Free Computations}
+
+ \begin{Definition}
+ A Turing machine is \alert{overhead-free} if
+ \begin{enumerate}
+ \item
+ it has only a single tape,
+ \item
+ writes only on input cells,
+ \item
+ writes only symbols drawn from the input alphabet.
+ \end{enumerate}
+ \end{Definition}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Overhead-Free Computation Complexity Classes}
+
+ \begin{Definition}
+ A language $L \subseteq \Sigma^*$ is in
+ \begin{description}
+ \item[\alert<1| handout:0| trans:0>{$\DOF$}%
+ {\note[item]<1>{Joke about German pronunciation}}]
+ if $L$ is accepted by a deterministic overhead-free machine with
+ input alphabet~$\Sigma$,
+ \pause
+ \item[\alert<2| handout:0| trans:0>{$\DOFpoly$}]
+ if $L$ is accepted by a deterministic overhead-free machine with
+ input alphabet~$\Sigma$ in polynomial time.
+ \pause
+ \item[\alert<3| handout:0| trans:0>{$\NOF$}]
+ is the nondeterministic version of $\DOF$,
+ \note[item]<3>{Stress meaning of D and N.}
+ \pause
+ \item[\alert<4| handout:0| trans:0>{$\NOFpoly$}]
+ is the nondeterministic version of $\DOFpoly$.
+ \end{description}
+ \end{Definition}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Simple Relationships among\\ Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{6cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{1.75cm}{2cm}{$\DOFpoly$}
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOF$}
+ \pgfheaplabeledcentered{2.5cm}{3.5cm}{$\NOFpoly$}
+ \pgfheaplabeledcentered{5cm}{4cm}{$\NOF$}
+
+ \pgfheaplabeledcentered{6cm}{5cm}{\raise10pt\hbox{}$\Class{NLINSPACE}$}
+ \end{pgfpicture}
+\end{frame}
+
+
+\section[Power of the Model]{The Power of Overhead-Free Computation}
+
+
+\subsection{Palindromes}
+
+\begin{frame}
+ \frametitle{Palindromes Can be Accepted in an Overhead-Free Way}
+
+ \begin{columns}
+
+ \column{4.5cm}
+ \begin{pgfpicture}{-0.5cm}{1cm}{4cm}{7cm}
+ \only<1| trans:1>{
+ \putmachinea{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{1}}
+ \only<2| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{2}}
+ \only<3| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{8}}
+ \only<4| handout:0| trans:2>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{1}
+ \selectpos{7}}
+ \only<5| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{1}{0}{1}{0}{0}{1}{0}{1}
+ \selectpos{1}}
+ \only<6| handout:0| trans:3>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{1}{1}{0}{0}{1}{0}{1}
+ \selectpos{2}}
+ \only<7| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{1}{1}{0}{0}{1}{0}{1}
+ \selectpos{8}}
+ \only<8| handout:0| trans:4>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{1}{1}{0}{0}{1}{1}{0}
+ \selectpos{7}}
+ \only<9| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{1}{1}{0}{0}{1}{1}{0}
+ \selectpos{2}}
+ \only<10| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{1}{0}
+ \selectpos{3}}
+ \only<11| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{1}{0}
+ \selectpos{7}}
+ \only<12| handout:0| trans:5>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{6}}
+ \only<13| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{1}{0}{0}{1}{0}{0}
+ \selectpos{3}}
+ \only<14| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{0}{1}{0}{1}{0}{0}
+ \selectpos{4}}
+ \only<15| handout:0| trans:0>{
+ \putmachineworkinga{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{0}{1}{0}{1}{0}{0}
+ \selectpos{6}}
+ \only<16| handout:0| trans:6>{
+ \putmachinea{\pgfxy(1.75,3)}{overhead-free machine}
+ \tape{\pgfxy(0,5)}{0}{0}{0}{1}{1}{0}{0}{0}
+ \selectpos{5}}
+ \end{pgfpicture}
+
+ \column{6cm}
+ \begin{block}{Algorithm}
+ \alert<1| handout:0| trans:1>{Phase 1:\\
+ Compare first and last bit}
+
+ \quad \alert<2| handout:0| trans:2>{Place left end marker}
+
+ \quad \alert<3| handout:0| trans:2>{Place right end marker}
+ \vskip1em
+
+ \alert<4| handout:0| trans:3->{Phase 2:\\
+ Compare bits next to end markers}
+
+ \quad \alert<5,9,13| handout:0| trans:0>{Find left end marker}
+
+ \quad \alert<6,10,14| handout:0| trans:0>{Advance left end marker}
+
+ \quad \alert<7,11,15| handout:0| trans:0>{Find right end marker}
+
+ \quad \alert<8,12,16| handout:0| trans:0>{Advance right end marker}
+
+ \end{block}
+ \end{columns}
+ \note<1>{Use 3 minutes.}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Relationships among Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{1.75cm}{2cm}{$\DOFpoly$}
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOF$}
+ \pgfheaplabeledcentered{2.5cm}{3.5cm}{$\NOFpoly$}
+ \pgfheaplabeledcentered{5cm}{4cm}{$\NOF$}
+
+ \pgfputat{\pgfxy(0,0.25)}{\pgfbox[center,base]{\alert{Palindromes}}}
+ \end{pgfpicture}
+\end{frame}
+
+
+\subsection{Linear Languages}
+
+\begin{frame}
+ \frametitle{A Review of Linear Grammars}
+
+ \begin{Definition}<1>
+ A grammar is \alert{linear} if it is context-free and\\ there is
+ only one nonterminal per right-hand side.
+ \end{Definition}
+
+ \begin{Example}<1>
+ $G_1\colon S \to 00S0 \mid 1$ and $G_2\colon S \to 0S10 \mid 0$.
+ \end{Example}
+
+ \begin{Definition}<2->
+ A grammar is \alert{deterministic} if\\ ``there is always only one
+ rule that can be applied.''
+ \note<2>{Just explain intution.}
+ \end{Definition}
+
+ \begin{Example}<2->
+ $G_1\colon S \to 00S0 \mid 1$ is deterministic.
+
+ $G_2\colon S \to 0S10 \mid 0$ is \alert{not} deterministic.
+ \end{Example}
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{Deterministic Linear Languages\\ Can Be Accepted in an
+ Overhead-Free Way}
+
+ \begin{Theorem}
+ Every deterministic linear language is in $\DOFpoly$.
+ \end{Theorem}
+\end{frame}
+
+\begin{frame}[<+->]
+ \frametitle{Metalinear Languages\\ Can Be Accepted in an
+ Overhead-Free Way}
+
+ \begin{Definition}
+ A language is \alert{metalinear} if it is the concatenation\\ of
+ linear languages.
+ \end{Definition}
+
+ \begin{Example}
+ $\Lang{triple-palindrome} = \Set{uvw \mid \text{$u$, $v$, and $w$ are palindromes}}$.
+ \end{Example}
+
+ \begin{Theorem}
+ Every metalinear language is in $\NOFpoly$.
+ \end{Theorem}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Relationships among Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOFpoly$}
+ \pgfheaplabeledcentered{4.25cm}{4cm}{$\NOFpoly$}
+ \pgfheaplabeledcentered{5cm}{5cm}{$\NOF$}
+
+ \color{red}%
+ \pgfheaplabeledcentered{1.75cm}{2cm}{\raise10pt\hbox{}deterministic}
+ \pgfheaplabeledcentered{2.5cm}{3.5cm}{metalinear}
+
+ \pgfputat{\pgfxy(0,0.6)}{\pgfbox[center,base]{linear}}
+ \end{pgfpicture}
+ \note[item]{Skip next subsection if more than 18 minutes have passed.}
+\end{frame}
+
+
+\subsection[Forbidden Subword]{Context-Free Languages with a Forbidden Subword}
+
+\begin{frame}
+ \frametitle{Definition of Almost-Overhead-Free Computations}
+
+ \begin{Definition}
+ A Turing machine is \alert{almost-overhead-free} if
+ \begin{enumerate}[<+-| alert@+>]
+ \item it has only a single tape,
+ \item writes only on input cells,
+ \item writes only symbols drawn from the input alphabet\\
+ plus one special symbol.
+ \end{enumerate}
+ \end{Definition}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Context-Free Languages with a Forbidden Subword\\ Can Be
+ Accepted in an Overhead-Free Way}
+
+ \begin{Theorem}
+ Let $L$ be a context-free language with a forbidden word.\\
+ Then $L \in \NOFpoly$.
+ \end{Theorem}
+
+ \begin{overprint}
+ \onslide<1| handout:0| trans:0| article:0>
+ \hfill\hyperlinkframestartnext{\beamerskipbutton{Skip proof}}
+ \onslide<2| handout:1| trans:1>
+ \begin{proof}
+ Every context-free language can be accepted by a nondeterministic
+ almost-overhead-free machine in polynomial time.
+ \end{proof}
+ \end{overprint}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Relationships among Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{5cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOFpoly$}
+ \pgfheaplabeledcentered{4.25cm}{4cm}{$\NOFpoly$}
+ \pgfheaplabeledcentered{5cm}{5cm}{$\NOF$}
+
+ \color{red}%
+ \pgfheaplabeledcentered{2.5cm}{3.5cm}{CFL with}
+
+ \pgfputat{\pgfxy(0,1.6)}{\pgfbox[center,base]{forbidden subwords}}
+ \end{pgfpicture}
+\end{frame}
+
+
+
+\subsection[Complete Languages]{Languages Complete for Polynomial Space}
+
+\begin{frame}<1>[label=pspacecomplete]
+ \frametitle{Overhead-Free Languages can be PSPACE-Complete}
+
+ \begin{Theorem}
+ $\DOF$ contains languages that are complete for
+ $\Class{PSPACE}$.
+ \end{Theorem}
+
+ \only<1| article:0| trans:0| handout:0>
+ {
+ \vskip1em
+
+ \hyperlink{pspacecomplete<2>}{\beamergotobutton{Proof details}}
+ }
+ \only<2>
+ {% this is only shown in the appendix, where this frame is resumed.
+ \begin{proof}
+ \begin{enumerate}
+ \item
+ Let $A \in \Class{DLINSPACE}$ be $\Class{PSPACE}$-complete.\\
+ Such languages are known to exist.
+ \item
+ Let $M$ be a linear space machine that accepts~$A \subseteq
+ \Set{0,1}^*$ with tape alphabet~$\Gamma$.
+ \item
+ Let $h \colon \Gamma \to \Set{0,1}^*$ be an isometric, injective
+ homomorphism.
+ \item
+ Then $h(L)$ is in $\Class{DOF}$ and it is
+ $\Class{PSPACE}$-complete. \qedhere
+ \end{enumerate}
+ \end{proof}
+
+ \only<beamer>{\hfill\hyperlink{pspacecomplete<1>}{\beamerreturnbutton{Return}}}
+ }
+\end{frame}
+
+\begin{frame}
+ \frametitle{Relationships among Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{6cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{1.75cm}{2cm}{$\DOFpoly$}
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOF$}
+ \pgfheaplabeledcentered{2.5cm}{3.5cm}{$\NOFpoly$}
+ \pgfheaplabeledcentered{5cm}{4cm}{$\NOF$}
+
+ \pgfsetdash{{3pt}{3pt}}{0pt}
+ \pgfheaplabeled{\pgfxy(0,2.9)}{\pgfxy(-5,6)}{\pgfxy(5,6)}{}%
+ \pgfputat{\pgfxy(-4.6,5.75)}{\pgfbox[left,base]{$\Class{PSPACE}\!\text{-hard}$}}%
+ \end{pgfpicture}
+\end{frame}
+
+
+\section[Limitations of the Model]{Limitations of Overhead-Free Computation}
+
+
+\subsection[Strict Inclusion]{Linear Space is Strictly More Powerful}
+
+\begin{frame}
+ \frametitle{Some Context-Sensitive Languages\\
+ Cannot be Accepted in an Overhead-Free Way}
+
+ \begin{Theorem}
+ $\DOF \subsetneq \Class{DLINSPACE}$.
+ \end{Theorem}
+
+ \begin{Theorem}
+ $\NOF \subsetneq \Class{NLINSPACE}$.
+ \end{Theorem}
+
+ \vskip1em
+ The proofs are based on old diagonalisations due to Feldman, Owings,
+ and Seiferas.
+\end{frame}
+
+\begin{frame}
+ \frametitle{Relationships among Overhead-Free Computation Classes}
+
+ \begin{pgfpicture}{-5.4cm}{0cm}{5.4cm}{6cm}
+ \pgfsetlinewidth{0.8pt}
+ \pgfxyline(-5,0)(5,0)
+
+ \pgfsetlinewidth{0.4pt}
+
+ \pgfheaplabeledcentered{3.5cm}{3cm}{$\DOF$}
+ \pgfheaplabeledcentered{5cm}{4cm}{$\NOF$}
+
+ \pgfheaplabeledcentered{4.3cm}{4.5cm}{\raise8pt\hbox{}$\Class{DLINSPACE}$}
+ \pgfheaplabeledcentered{6cm}{5cm}{\raise10pt\hbox{}$\Class{NLINSPACE}$}
+
+ \pgfsetdash{{3pt}{3pt}}{0pt}
+ \pgfheaplabeled{\pgfxy(0,2.9)}{\pgfxy(-5,6)}{\pgfxy(5,6)}{}%
+ \pgfputat{\pgfxy(-4.6,5.75)}{\pgfbox[left,base]{$\Class{PSPACE}$-hard}}%
+ \end{pgfpicture}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Candidates for Languages that\\
+ Cannot be Accepted in an Overhead-Free Way}
+
+ \begin{overprint}
+ \onslide<all:1>
+ \begin{block}{Conjecture}
+ \strut
+ $\Lang{double-palindromes} \notin \Class{DOF}$.
+ \end{block}
+
+ \onslide<all:2>
+ \begin{alertblock}{Theorem\vphantom{j}}
+ \strut
+ $\Lang{double-palindromes} \in \Class{DOF}$.
+ \end{alertblock}
+ \end{overprint}
+
+ \begin{block}{Conjecture}
+ $\Set{ww \mid w\in \Set{0,1}^*} \notin \Class{NOF}$.
+ \end{block}
+
+ \vskip1em
+ \uncover<1>{Proving the first conjecture would show $\Class{DOF} \subsetneq
+ \Class{NOF}$.}
+\end{frame}
+
+
+\section*{Summary}
+
+\subsection<presentation>*{Summary}
+
+\begin{frame}
+ \frametitle<presentation>{Summary}
+
+ \begin{block}{}
+ \begin{itemize}
+ \item
+ Overhead-free computation is a more faithful\\
+ \alert{model of fixed-size memory}.
+ \item
+ Overhead-free computation is \alert{less powerful} than linear space.
+ \item
+ \alert{Many} context-free languages can be accepted\\
+ by overhead-free machines.
+ \item
+ We conjecture that \alert{all} context-free languages are in
+ $\NOFpoly$.
+ \item
+ Our results can be seen as new results on the power of\\
+ \alert{linear bounded automata with fixed alphabet} size.
+ \end{itemize}
+ \end{block}
+
+ \note[item]{Point out result concerning all context-free languages.}
+ \note[item]{Relationship to restart automata.}
+\end{frame}
+
+
+
+\subsection<presentation>*{Further Reading}
+
+\begin{frame}
+ \frametitle<presentation>{For Further Reading}
+
+ \beamertemplatebookbibitems
+
+ \begin{thebibliography}{10}
+
+ \bibitem{sal:b:formal-languages}
+ A.~Salomaa.
+ \newblock {\em Formal Languages}.
+ \newblock Academic Press, 1973.
+ \pause
+
+ \beamertemplatearticlebibitems
+ \bibitem{dij:j:smoothsort}
+ E.~Dijkstra.
+ \newblock Smoothsort, an alternative for sorting in situ.
+ \newblock {\em Science of Computer Programming}, 1(3):223--233,
+ 1982.
+ \pause
+
+ \bibitem{FeldmanO1973}
+ E.~Feldman and J.~Owings, Jr.
+ \newblock A class of universal linear bounded automata.
+ \newblock {\em Information Sciences}, 6:187--190, 1973.
+ \pause
+
+ \bibitem{JancarMPV1995}
+ P.~Jan{\v c}ar, F.~Mr{\'a}z, M.~Pl{\'a}tek, and J.~Vogel.
+ \newblock Restarting automata.
+ \newblock {\em FCT Conference 1995}, LNCS 985, pages
+ 282--292. 1995.
+ \end{thebibliography}
+\end{frame}
+
+
+%
+% The following appendix material is not shown in the normal course of
+% the presentation
+%
+
+\appendix
+
+\AtBeginSubsection{}
+
+
+\section{\appendixname}
+
+\frame{\frametitle{Appendix Outline}\tableofcontents}
+
+
+\subsection{Complete Languages}
+
+\againframe<beamer| beamer:2>{pspacecomplete}
+
+
+\subsection{Improvements for Context-Free Languages}
+
+\begin{frame}
+ \frametitle{Improvements}
+
+ \begin{theorem}
+ \begin{enumerate}
+ \item
+ $\Class{DCFL} \subseteq \DOFpoly$.
+ \item
+ $\Class{CFL} \subseteq \NOFpoly$.
+ \end{enumerate}
+ \end{theorem}
+\end{frame}
+
+
+\subsection{Abbreviations}
+
+\begin{frame}
+ \frametitle{Explanation of Different Abbreviations}
+
+ \begin{table}
+ \rowcolors[]{1}{structure!25!averagebackgroundcolor}{structure!10!averagebackgroundcolor}
+ \begin{tabular}{ll}
+ \structure{$\DOF$} & \structure{D}eterministic \structure{O}verhead-\structure{F}ree.\\
+ \structure{$\NOF$} & \structure{N}ondeterministic \structure{O}verhead-\structure{F}ree.\\
+ \structure{$\DOFpoly$} & \structure{D}eterministic
+ \structure{O}verhead-\structure{F}ree, \structure{poly}nomial time.\\
+ \structure{$\DOFpoly$} & \structure{N}ondeterministic \structure{O}verhead-\structure{F}ree, \structure{poly}nomial time.
+ \end{tabular}
+ \caption{Explanation of what different abbreviations mean.}
+ \end{table}
+\end{frame}
+
+\end{document}
+
+