[subversion-commit] SVN tetex-src commit + diffs: r1757 - in
tetex-src/trunk: . debian source/fonts/fpl source/generic
source/generic/pstricks/contrib/pst-3dplot
source/generic/pstricks/contrib/pstricks-add/examples
source/generic/ruhyphen source/latex source/latex/beamer/doc
source/latex/beamer/examples source/latex/beamer/lyx/examples
source/latex/bibunits source/latex/changebar
source/latex/koma-script source/latex/multibib
source/latex/ps4pdf source/latex/textpos/t
Frank Küster
frank at costa.debian.org
Mon Oct 9 21:00:52 UTC 2006
Author: frank
Date: 2006-10-09 21:00:50 +0000 (Mon, 09 Oct 2006)
New Revision: 1757
Added:
tetex-src/trunk/README.Debian-source
Removed:
tetex-src/trunk/Makefile
tetex-src/trunk/hypdoc/
tetex-src/trunk/source/latex/beamer/examples/beamer-computer-mask.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-computer.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-computerred.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-g4-mask.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-g4.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-g4red.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-ram-mask.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-ram.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-tu-logo-mask.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-tu-logo.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-ur-logo-mask.jpg
tetex-src/trunk/source/latex/beamer/examples/beamer-ur-logo.jpg
tetex-src/trunk/source/latex/beamer/examples/beamerexample1.pdf
tetex-src/trunk/source/latex/beamer/examples/beamerexample1.tex
tetex-src/trunk/source/latex/beamer/examples/beamerexample5.pdf
tetex-src/trunk/source/latex/beamer/examples/beamerexample5.tex
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-icsi-logo.pdf
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight1-mask.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight1.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight2-mask.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight2.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight3-mask.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight3.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight4-mask.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamer-knight4.png
tetex-src/trunk/source/latex/beamer/lyx/examples/beamerlyxexample1.lyx
Modified:
tetex-src/trunk/debian/changelog
tetex-src/trunk/debian/rules
tetex-src/trunk/source/fonts/fpl/TeXPalladioL-BoldItalicOsF.pe
tetex-src/trunk/source/fonts/fpl/TeXPalladioL-BoldOsF.pe
tetex-src/trunk/source/fonts/fpl/TeXPalladioL-ItalicOsF.pe
tetex-src/trunk/source/fonts/fpl/TeXPalladioL-SC.pe
tetex-src/trunk/source/generic/install-files
tetex-src/trunk/source/generic/pstricks/contrib/pst-3dplot/install
tetex-src/trunk/source/generic/pstricks/contrib/pstricks-add/examples/dataI.dat
tetex-src/trunk/source/generic/pstricks/contrib/pstricks-add/examples/dataII.dat
tetex-src/trunk/source/generic/ruhyphen/mkcyryo
tetex-src/trunk/source/generic/ruhyphen/reduce-patt
tetex-src/trunk/source/generic/ruhyphen/sorthyph
tetex-src/trunk/source/generic/ruhyphen/sortkoi8
tetex-src/trunk/source/generic/ruhyphen/trans
tetex-src/trunk/source/generic/unimap.py
tetex-src/trunk/source/latex/beamer/doc/beameruserguide.pdf
tetex-src/trunk/source/latex/bibunits/bibtexall
tetex-src/trunk/source/latex/changebar/chbar.sh
tetex-src/trunk/source/latex/install-files
tetex-src/trunk/source/latex/koma-script/genindex.pl
tetex-src/trunk/source/latex/multibib/bibtexall
tetex-src/trunk/source/latex/ps4pdf/create-eps
tetex-src/trunk/source/latex/textpos/t/runtests
Log:
new repackaged, free tarball
Deleted: tetex-src/trunk/Makefile
===================================================================
--- tetex-src/trunk/Makefile 2006-10-09 20:57:52 UTC (rev 1756)
+++ tetex-src/trunk/Makefile 2006-10-09 21:00:50 UTC (rev 1757)
@@ -1,51 +0,0 @@
-#!/usr/bin/make
-
-# Makefile to create source2.dtx with hyperref extensions
-# Copyright 2005 Frank Küster <frank at kuesterei.ch>
-# This file is in the public domain, you can freely use,
-# distribute and/or modify it
-
-all: source2e/source2e.pdf
-
-source2e/source2e.pdf: setup-source2e source2e/source2e.tex
- (cd source2e; $(createpdf))
-
-source2e/hypdoc.sty: source2e hypdoc/hypdoc.dtx
- cd hypdoc; tex hypdoc.dtx
- mv hypdoc/hypdoc.sty source2e
-
-hypdoc/hypdoc.dtx: hypdoc/hypdoc.pdf
- cd hypdoc; pdftk hypdoc.pdf unpack_files output .
-
-hypdoc/hypdoc.pdf.uu:
- uuencode < hypdoc/hypdoc.pdf hypdoc/hypdoc.pdf.uu > hypdoc/hypdoc.pdf.uu
- rm hypdoc/hypdoc.pdf
-
-hypdoc/hypdoc.pdf:
- uudecode -o hypdoc/hypdoc.pdf hypdoc/hypdoc.pdf.uu
-
-setup-source2e: source2e patch-stamp
-
-patch-stamp: source2e source2e/hypdoc.sty
- patch -p0 -i hypdoc/source2e-hypdoc.patch
- touch patch-stamp
-
-source2e:
- cp -a source/latex/base source2e
-# (cd hypdoc; latex hypdoc.ins)
-# mv hypdoc/hypdoc.sty source2e/
-
-
-clean:
- rm -rf source2e
- -rm hypdoc/hypdoc.drv hypdoc/hypdoc.ins hypdoc/hypdoc.log hypdoc/hypdoc.dtx
- -rm patch-stamp
-
-
-define createpdf
-pdflatex source2e; \
-makeindex -s source2e.ist source2e.idx; \
-makeindex -s gglo.ist -o source2e.gls source2e.glo; \
-pdflatex source2e; \
-pdflatex source2e
-endef
Copied: tetex-src/trunk/README.Debian-source (from rev 1756, tetex-src/branches/upstream/current/README.Debian-source)
===================================================================
--- tetex-src/trunk/README.Debian-source (rev 0)
+++ tetex-src/trunk/README.Debian-source 2006-10-09 21:00:50 UTC (rev 1757)
@@ -0,0 +1,7 @@
+The following files and directories are non-free (or contrib, using
+the non-free files) and had to be removed:
+
+source/latex/beamer/lyx/examples/*
+source/latex/beamer/examples/*jpg
+source/latex/beamer/examples/beamerexample1.{tex,pdf}
+source/latex/beamer/examples/beamerexample5.{tex,pdf}
Modified: tetex-src/trunk/debian/changelog
===================================================================
--- tetex-src/trunk/debian/changelog 2006-10-09 20:57:52 UTC (rev 1756)
+++ tetex-src/trunk/debian/changelog 2006-10-09 21:00:50 UTC (rev 1757)
@@ -1,3 +1,9 @@
+tetex-src (3.0.dfsg.1-1) UNRELEASED; urgency=low
+
+ * (NOT RELEASED YET) New upstream release
+
+ -- Frank Küster <frank at kuesterei.ch> Mon, 9 Oct 2006 22:58:28 +0200
+
tetex-src (3.0-3.1) UNRELEASED; urgency=low
* Move debhelper from Build-Depends-Indep to Build-Depends, it is used
Modified: tetex-src/trunk/debian/rules
===================================================================
--- tetex-src/trunk/debian/rules 2006-10-09 20:57:52 UTC (rev 1756)
+++ tetex-src/trunk/debian/rules 2006-10-09 21:00:50 UTC (rev 1757)
@@ -49,7 +49,7 @@
cat debian/$(SOURCE2EPAC).copyright.Debian source2e/legal.txt source2e/lppl.txt > $(SOURCE2EDOC)/copyright
# remove all executable bits
- find DEBTEXMF=$(SRCDIR)/debian/tetex-src/usr/share/texmf-tetex -type f -perm +1 | xargs chmod a-x
+ find $(SRCDIR)/debian/tetex-src/usr/share/texmf-tetex -type f -perm +1 | xargs chmod a-x
# Build architecture-dependent files here.
binary-arch: build install
Property changes on: tetex-src/trunk/source/fonts/fpl/TeXPalladioL-BoldItalicOsF.pe
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/fonts/fpl/TeXPalladioL-BoldOsF.pe
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/fonts/fpl/TeXPalladioL-ItalicOsF.pe
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/fonts/fpl/TeXPalladioL-SC.pe
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/install-files
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/pstricks/contrib/pst-3dplot/install
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/pstricks/contrib/pstricks-add/examples/dataI.dat
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/pstricks/contrib/pstricks-add/examples/dataII.dat
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/ruhyphen/mkcyryo
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/ruhyphen/reduce-patt
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/ruhyphen/sorthyph
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/ruhyphen/sortkoi8
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/ruhyphen/trans
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/generic/unimap.py
___________________________________________________________________
Name: svn:executable
-
+ *
Property changes on: tetex-src/trunk/source/latex/beamer/doc/beameruserguide.pdf
___________________________________________________________________
Name: svn:executable
-
+ *
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-computer-mask.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-computer.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-computerred.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-g4-mask.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-g4.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-g4red.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-ram-mask.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-ram.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-tu-logo-mask.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-tu-logo.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-ur-logo-mask.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamer-ur-logo.jpg
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamerexample1.pdf
===================================================================
(Binary files differ)
Deleted: tetex-src/trunk/source/latex/beamer/examples/beamerexample1.tex
===================================================================
--- tetex-src/trunk/source/latex/beamer/examples/beamerexample1.tex 2006-10-09 20:57:52 UTC (rev 1756)
+++ tetex-src/trunk/source/latex/beamer/examples/beamerexample1.tex 2006-10-09 21:00:50 UTC (rev 1757)
@@ -1,941 +0,0 @@
-% $Header: /cvsroot/latex-beamer/latex-beamer/examples/beamerexample1.tex,v 1.46 2004/10/07 20:53:07 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 at 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 at +>]
- \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}
-
-
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-\title{Weak Cardinality Theorems for First-Order Logic}
-\author{Till Tantau}
-\institute[Technische Universit\"at Berlin]{%
- Fakultät für Elektrotechnik und Informatik\\
- Technische Universit\"at Berlin}
-\date{Fundamentals of Computation Theory 2003}
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-\AtBeginSection[]{\frame{\frametitle{Outline}\tableofcontents[current]}}
-
-\begin{document}
-
-\frame{\titlepage}
-
-%\section*{Outline}
-\part{Main Part}
-\frame{\frametitle{Outline}\tableofcontents[part=1]}
-
-\section{History}
-
-\subsection{Enumerability in Recursion and Automata Theory}
-
-\frame
-{
- \frametitle{Motivation of Enumerability}
-
- \begin{block}{Problem}
- Many functions are not computable or not efficiently computable.
- \end{block}
- \vskip-1em
- \begin{overprint}
- \onslide<1-2>
- \begin{example}
- \begin{overprint}
- \onslide<1>
- \vskip0.5em
- \begin{itemize}
- \item
- $\NumSAT$:\\
- How many satisfying assignments does a formula have?
- \end{itemize}
-
- \onslide<2>
- \vskip0.5em
- For difficult languages~$A$:
- \begin{itemize}
- \item
- Cardinality function $\NumA^n$:\\
- \alert{How many} input words are in~$A$?
- \item
- Characteristic function $\chi_A^n$:\\
- \alert{Which} input words are in~$A$?
- \end{itemize}
- \begin{pgfpicture}{-9cm}{0.75cm}{-9cm}{2cm}
-
- \pgfnodebox{words}[virtual]{\pgfxy(0,3.5)}{$(w_1, \alert{w_2},
- w_3, w_4, \alert{w_5})$}{2pt}{5pt}
-
- \color{red}
- \pgfputat{\pgfxy(0.75,4.5)}{\pgfbox[center,base]{in $A$}}
- \pgfxyline(0.75,4.4)(-0.6,3.7)
- \pgfxyline(0.75,4.4)(1.2,3.7)
- \color{black}
-
- \pgfnodebox{number}[virtual]{\pgfxy(-1,1)}{2}{2pt}{2pt}
- \pgfnodebox{string}[virtual]{\pgfxy(1,1)}{0\alert{1}00\alert{1}}{2pt}{2pt}
-
- \pgfsetstartarrow{\pgfarrowbar}
- \pgfsetendarrow{\pgfarrowto}
-
- \pgfnodeconnline{words}{string}%{-60}{120}{1cm}{1cm}
- \pgfnodeconnline{words}{number}%{-120}{60}{1cm}{1cm}
-
- \pgfputat{\pgfxy(-0.9,2.3)}{\pgfbox[center,base]{$\NumA^5$}}
- \pgfputat{\pgfxy(0.9,2.3)}{\pgfbox[center,base]{$\chi_A^5$}}
- \end{pgfpicture}
- \end{overprint}
- \end{example}
-
- \onslide<3>
- \begin{block}{Solutions}
- Difficult functions can be
- \begin{itemize}
- \item
- computed using probabilistic algorithms,
- \item
- computed efficiently on average,
- \item
- approximated, or
- \item<alert at 1->
- enumerated.
- \end{itemize}
- \end{block}
- \end{overprint}
-}
-
-\frame
-{
- \frametitle{Enumerators Output Sets of Possible Function Values}
- \begin{columns}
- \begin{column}{4.5cm}
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-
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- \only<4->{\Slot{1.8cm}}
-
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- \pgfxyline(2,0.5)(2,1)
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-
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- \end{pgfpicture}
- \end{column}
- \begin{column}{6.5cm}
- \begin{definition}[1987, 1989, 1994, 2001]
- An \alert{$m$-enumerator} for a function~$f$
- \begin{enumerate}
- \item<alert at 1-4>
- reads $n$ input words $w_1$, \dots, $w_n$,
- \item<alert at 5>
- does a computation,
- \item<alert at 6-8>
- outputs at most $m$ values,
- \item<alert at 9>
- one of which is $f(w_1,\dots,w_n)$.
- \end{enumerate}
- \end{definition}
- \end{column}
- \end{columns}
-}
-
-\subsection{Known Weak Cardinality Theorem}
-
-\frame
-{
- \frametitle{How Well Can the Cardinality Function Be Enumerated?}
-
- \begin{block}{Observation}
- For fixed~$n$, the cardinality function $\NumA^n$
- \begin{itemize}
- \item
- can be \alert{$1$}-enumerated by Turing machines only for \alert{recursive}~$A$,~but\hskip-0.5cm\hbox{}
- \item
- can be \alert{$(n+1)$}-enumerated for \alert{every} language~$A$.
- \end{itemize}
- \end{block}
-
- \begin{alertblock}{Question}<2->
- What about $2$-, $3$-, $4$-, \dots, $n$-enumerability?
- \end{alertblock}
-}
-
-\newtheorem{card}{Cardinality Theorem}[theorem]
-\newtheorem{weakcard}{Weak Cardinality Theorems}[theorem]
-
-\frame
-{
- \frametitle{How Well Can the Cardinality Function\\ Be Enumerated
- by Turing Machines?}
-
- \begin{card}[Kummer, 1992]
- If $\NumA^n$ is $n$-enumerable by a Turing machine, then $A$ is
- recursive.
- \end{card}
-
- \begin{weakcard}[\uncover<2->{\alert<1-2>{1987},} \uncover<3->{\alert<3>{1989},}
- \uncover<4->{\alert<4>{1992}}]<2->
- \begin{enumerate}
- \item<2-| alert at 2>
- If $\chi_A^n$ is $n$-enumerable by a Turing machine, then $A$ is
- recursive.
- \item<3-| alert at 3>
- If $\NumA^2$ is $2$-enumerable by a Turing machine, then $A$ is
- recursive.
- \item<4-| alert at 4>
- If $\NumA^n$ is $n$-enumerable by a Turing machine that never
- enumerates both $0$ and~$n$, then $A$ is recursive.
- \end{enumerate}
- \end{weakcard}
-}
-
-
-\frame
-{
- \frametitle{How Well Can the Cardinality Function\\ Be Enumerated
- by Finite Automata?}
-
- \begin{alertblock}{Conjecture}
- If $\NumA^n$ is $n$-enumerable by a \alert{finite automaton}, then $A$ is
- \alert{regular}.
- \end{alertblock}
-
- \begin{weakcard}[2001, 2002]
- \begin{enumerate}
- \item
- If $\chi_A^n$ is $n$-enumerable by a \alert{finite automaton}, then $A$ is
- \alert{regular}.
- \item
- If $\NumA^2$ is $2$-enumerable by a \alert{finite automaton}, then $A$ is
- \alert{regular}.
- \item
- If $\NumA^n$ is $n$-enumerable by a \alert{finite automaton} that never
- enumerates both $0$ and~$n$, then $A$ is \alert{regular}.
- \end{enumerate}
- \end{weakcard}
-}
-
-
-\subsection{Why Do Cardinality Theorems Hold Only for Certain Models?}
-
-\frame
-{
- \frametitle{Cardinality Theorems Do Not Hold for All Models}
-
- \begin{pgfpicture}{-2.5cm}{0.3cm}{0.5cm}{6.5cm}
- \pgfsetlinewidth{0.6pt}
-
- \pgfsetendarrow{\pgfarrowto}
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- \pgfclearendarrow
-
- \pgfputat{\pgfxy(-0.2,5.75)}{\pgfbox[right,base]{Turing machines}}
-
- \only<2>{
- \pgfputat{\pgfxy(-0.2,3.75)}{\pgfbox[right,base]{\alert{resource-bounded}}}
- \pgfputat{\pgfxy(-0.2,3.25)}{\pgfbox[right,base]{\alert{machines}}}
- \pgfcircle[fill]{\pgfxy(0,3.6)}{2pt}
- \pgfputat{\pgfxy(0.4,3.5)}{\pgfbox[left,base]{Weak cardinality
- theorems do \alert{not} hold.}}}
-
- \pgfputat{\pgfxy(-0.2,1.5)}{\pgfbox[right,base]{finite}}
- \pgfputat{\pgfxy(-0.2,1)}{\pgfbox[right,base]{automata}}
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- \pgfcircle[fill]{\pgfxy(0,1.35)}{2pt}
-
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- theorems hold.}}
- \end{pgfpicture}
-}
-
-\frame
-{
- \frametitle{Why?}
-
- \begin{block}{First Explanation}<1>
- The weak cardinality theorems hold both for recursion and automata
- theory \alert{by coincidence}.
- \end{block}
-
- \begin{block}{Second Explanation}<1-2>
- The weak cardinality theorems hold both for
- recursion and automata theory, \alert{because they are
- instantiations of\\ single, unifying theorems}.
- \end{block}
-
- \vskip1em
- \visible<2->{
- The second explanation is correct.\\
- The theorems can (almost) be unified using first-order logic.
- }
-}
-
-
-
-\section[Unification by Logic]{Unification by First-Order Logic}
-
-\subsection{Elementary Definitions}
-
-\frame
-{
- \frametitle{What Are Elementary Definitions?}
-
- \begin{definition}
- A relation~$R$ is \alert{elementarily definable in a
- logical structure~$\mathcal S$} if
- \begin{enumerate}
- \item
- there exists a first-order formula~$\phi$,
- \item
- that is true exactly for the elements of~$R$.
- \end{enumerate}
- \end{definition}
-
- \begin{example}
- The set of even numbers is elementarily definable in $(\Nat, +)$
- via the formula $\phi(x) \equiv \exists z \centerdot z+z=x$.
- \end{example}
-
- \begin{example}
- The set of powers of 2 is not elementarily definable in $(\Nat, +)$.
- \end{example}
-}
-
-
-\frame
-{
- \frametitle{Characterisation of Classes by Elementary Definitions}
-
- \begin{theorem}[B\"uchi, 1960]
- There exists a logical structure~$(\Nat, +, \mathrm e_2)$
- such that a set $A \subseteq \Nat$ is\\ \alert{regular} iff it is
- \alert{elementarily definable in~$(\Nat, +, \mathrm e_2)$}.
- \end{theorem}
-
- \begin{theorem}
- There exists a logical structure~$\mathcal R$ such that a set $A
- \subseteq \Nat$ is \alert{recursively enumerable} iff it is \alert{positively
- elementarily definable in~$\mathcal R$}.\hskip-0.5cm\hbox{}
- \end{theorem}
-}
-
-
-
-\frame
-{
- \frametitle{Characterisation of Classes by Elementary Definitions}
-
- \begin{pgfpicture}{-5.4cm}{0.3cm}{5.4cm}{6.5cm}
- \pgfsetlinewidth{0.6pt}
-
- \pgfsetendarrow{\pgfarrowto}
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-
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- \pgfcircle[fill]{\pgfxy(0,3.6)}{2pt}
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-
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-
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- \pgfputat{\pgfxy(0.3,5.5)}{\pgfbox[left,base]{$(\mathrm{On}, +, \cdot)$}}}
- \end{pgfpicture}
-}
-
-
-\subsection{Enumerability for First-Order Logic}
-
-\frame
-{
- \frametitle{Elementary Enumerability is a Generalisation of\\ Elementary Definability}
-
- \begin{columns}
- \begin{column}{3.25cm}
- \begin{pgfpicture}{-0.25cm}{0cm}{3cm}{4cm}
-
- \color{shaded}
- \pgfmoveto{\pgfxy(0,1.3)}
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- \pgfputat{\pgfxy(2.6,0)}{\pgfbox[left,center]{$x$}}
- \pgfputat{\pgfxy(0,3.2)}{\pgfbox[center,base]{$f(x)$}}
- \pgfputat{\pgfxy(2.55,2)}{\pgfbox[left,center]{$f$}}
- \end{pgfpicture}
- \end{column}
- \begin{column}{7.5cm}
- \begin{definition}
- A function~$f$ is\\
- \alert{elementarily $m$-enumerable in a structure~$\mathcal S$} if
- \begin{enumerate}
- \item
- its graph is contained in an\\
- \alert{elementarily definable} relation~$R$,
- \item
- which is \alert{$m$-bounded}, i.\kern1pt e., for each~$x$
- there are at most~$m$ different~$y$ with $(x,y) \in R$.
- \end{enumerate}
- \end{definition}
- \end{column}
- \end{columns}
-}
-
-\frame
-{
- \frametitle{The Original Notions of Enumerability are Instantiations}
-
- \begin{theorem}
- A function is $m$-enumerable by a \alert{finite automaton} iff\\
- it is elementarily $m$-enumerable in \alert{$(\Nat, +, \mathrm e_2)$}.
- \end{theorem}
-
- \begin{theorem}
- A function is $m$-enumerable by a \alert{Turing machine} iff\\
- it is positively elementarily $m$-enumerable in \alert{$\mathcal R$}.
- \end{theorem}
-}
-
-%\subsection{Cross Product Theorem for First-Order Logic}
-
-\subsection{Weak Cardinality Theorems for First-Order Logic}
-
-\frame
-{
- \frametitle{The First Weak Cardinality Theorem}
-
- \begin{theorem}
- Let $\mathcal S$ be a logical structure with universe~$U$ and let
- $A \subseteq U$. If
-
- \begin{enumerate}
- \item
- $\mathcal S$ is well-orderable and
- \item
- \alert{$\chi_A^n$} is elementarily \alert{$n$}-enumerable in~$\mathcal S$,
- \end{enumerate}
-
- then \alert{$A$ is elementarily definable} in~$\mathcal S$.
- \end{theorem}
- \begin{overprint}
- \onslide<2>
- \begin{corollary}
- If $\chi_A^n$ is $n$-enumerable by a finite automaton, then
- $A$ is regular.
- \end{corollary}
-
- \onslide<3>
- \begin{corollary}[with more effort]
- If $\chi_A^n$ is $n$-enumerable by a Turing machine, then $A$
- is recursive.
- \end{corollary}
- \end{overprint}
-}
-
-\frame
-{
- \frametitle{The Second Weak Cardinality Theorem}
-
- \begin{theorem}
- Let $\mathcal S$ be a logical structure with universe~$U$ and let
- $A \subseteq U$. If
-
- \begin{enumerate}
- \item
- $\mathcal S$ is well-orderable,
- \item
- every finite relation on~$U$ is elementarily definable
- in~$\mathcal S$, and
- \item
- \alert{$\NumA^2$} is elementarily \alert{$2$}-enumerable in~$\mathcal S$,
- \end{enumerate}
-
- then \alert{$A$ is elementarily definable} in~$\mathcal S$.
- \end{theorem}
-% \begin{overlayarea}{\textwidth}{2cm}
-% \only<2>{
-% \begin{corollary}
-% If $\NumA^2$ is $2$-enumerable by a finite automaton, then
-% $A$ is regular.
-% \end{corollary}}%
-% \only<3>{
-% \begin{block}{Corollary}
-% If $\NumA^2$ is $2$-enumerable by a Turing machine, then $A$
-% is recursive in the halting problem.
-% \end{block}
-% }
-% \end{overlayarea}
-}
-
-\frame
-{
- \frametitle{The Third Weak Cardinality Theorem}
-
- \begin{theorem}
- Let $\mathcal S$ be a logical structure with universe~$U$ and let
- $A \subseteq U$. If
-
- \begin{enumerate}
- \item
- $\mathcal S$ is well-orderable,
- \item
- every finite relation on~$U$ is elementarily definable
- in~$\mathcal S$, and
- \item
- \alert{$\NumA^n$} is elementarily \alert{$n$}-enumerable in~$\mathcal S$ via a
- relation that \alert{never `enumerates' both $0$ and~$n$},
- \end{enumerate}
-
- then \alert{$A$ is elementarily definable} in~$\mathcal S$.
- \end{theorem}
-% \begin{overlayarea}{\textwidth}{2cm}
-% \only<2>{
-% \begin{corollary}
-% If $\NumA^n$ is $n$-enumerable by a finite automaton that
-% never enumerates both $0$ and~$n$, then $A$ is regular.
-% \end{corollary}}%
-% \only<3>{
-% \begin{block}{Corollary}
-% If $\NumA^n$ is $n$-enumerable by a Turing machine that never
-% enumerates both $0$ and~$n$, then $A$ is recursive in the
-% halting problem.
-% \end{block}
-% }
-% \end{overlayarea}
-}
-
-
-
-\frame
-{
- \frametitle{Relationships Between Cardinality Theorems (CT)}
-
- \begin{pgfpicture}{0cm}{0cm}{10cm}{5cm}
- \only<2>{%
- \color{alert}
- \pgfnodebox{autX}[virtual]{\pgfxy(2.2,4)}{CT}{2pt}{2pt}
- \color{black}}%
- \pgfnodebox{autA}[virtual]{\pgfxy(1,3)}{1st Weak CT}{2pt}{2pt}
- \pgfnodebox{autB}[virtual]{\pgfxy(1,2)}{2nd Weak CT}{2pt}{2pt}
- \pgfnodebox{autC}[virtual]{\pgfxy(1,1)}{3rd Weak CT}{2pt}{2pt}
-
- \only<2>{%
- \color{alert}
- \pgfnodebox{logX}[virtual]{\pgfxy(6.2,4.5)}{CT}{2pt}{2pt}%
- \color{black}}%
- \pgfnodebox{logA}[virtual]{\pgfxy(5,3.5)}{1st Weak CT}{2pt}{2pt}
- \pgfnodebox{logB}[virtual]{\pgfxy(5,2.5)}{2nd Weak CT}{2pt}{2pt}
- \pgfnodebox{logC}[virtual]{\pgfxy(5,1.5)}{3rd Weak CT}{2pt}{2pt}
-
- \pgfnodebox{recX}[virtual]{\pgfxy(10.2,4)}{CT}{2pt}{2pt}
- \pgfnodebox{recA}[virtual]{\pgfxy(9,3)}{1st Weak CT}{2pt}{2pt}
- \pgfnodebox{recB}[virtual]{\pgfxy(9,2)}{2nd Weak CT}{2pt}{2pt}
- \pgfnodebox{recC}[virtual]{\pgfxy(9,1)}{3rd Weak CT}{2pt}{2pt}
-
- \pgfputat{\pgfxy(1,4.5)}{\pgfbox[center,base]{\structure{automata theory}}}
- \pgfputat{\pgfxy(5,5)}{\pgfbox[center,base]{\structure{first-order logic}}}
- \pgfputat{\pgfxy(9,4.5)}{\pgfbox[center,base]{\structure{recursion
- theory}}}
-
- {%
- \color{structure}%
- \pgfxyline(3,0)(3,5)
- \pgfxyline(7,0)(7,5)
- }%
- \pgfsetendarrow{\pgfarrowto}
- \pgfnodeconnline{logA}{autA}
- \pgfnodeconnline{logA}{recA}
- \pgfnodeconnline{logB}{autB}
- \pgfnodeconnline{logC}{autC}
-
- \pgfnodeconncurve{recX}{recA}{-60}{5}{10pt}{10pt}
- \pgfnodeconncurve{recX}{recB}{-55}{5}{10pt}{20pt}
- \pgfnodeconncurve{recX}{recC}{-50}{5}{10pt}{30pt}
-
- \only<2>{%
- \alert{
- \pgfnodeconnline{logX}{autX}
- \pgfnodeconncurve{logX}{logA}{-60}{0}{10pt}{10pt}
- \pgfnodeconncurve{logX}{logB}{-55}{0}{10pt}{20pt}
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- \pgfnodeconncurve{autX}{autC}{-50}{11}{10pt}{30pt}
- }
- }
-
- \pgfsetdash{{3pt}{3pt}}{0pt}
- \pgfnodeconnline{logB}{recB}
- \pgfnodeconnline{logC}{recC}
-
- \only<2>{%
- \alert{\pgfnodeconnline{logX}{recX}}}
- \end{pgfpicture}
-}
-
-
-\section{Applications}
-
-\subsection{A Separability Result for First-Order Logic}
-
-%\frame
-%{
-% \begin{columns}
-% \begin{column}{2.4cm}
-% \begin{pgfpicture}{-1.2cm}{-1.2cm}{1cm}{1cm}
-% \color{shaded}
-% \pgfrect[fill]{\pgfxy(-1.4,-1)}{\pgfxy(2.8,2)}
-
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-% \pgfcircle[fill]{\pgfxy(-0.6,0)}{0.5cm}
-% \pgfcircle[fill]{\pgfxy(0.6,0)}{0.5cm}
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-% \pgfcircle[fill]{\pgfxy(-0.6,0)}{0.6cm}}%
-% %
-% \color{black}
-% \pgfcircle[stroke]{\pgfxy(-0.6,0)}{0.5cm}
-% \pgfcircle[stroke]{\pgfxy(0.6,0)}{0.5cm}
-
-% \pgfputat{\pgfxy(-0.6,0)}{\pgfbox[center,center]{$A^{(n)}$}}
-% \pgfputat{\pgfxy(0.6,0)}{\pgfbox[center,center]{$\barA{}^{(n)}$}}
-% \end{pgfpicture}
-% \end{column}
-% \begin{column}{8cm}
-% \begin{block}{Notation}
-% Let $A^{(n)}$ contain all $n$ tuples of\\
-% distinct elements of~$A$.
-% \end{block}
-
-% \begin{block}{Theorem}
-% Let $\mathcal S$ be a well-orderable logical structure in which
-% all finite relations are elementarily definable.\\[0.5em]
-% If $A^{(n)}$ and $\barA{}^{(n)}$ are \alert<2>{elementarily separable}
-% in~$\mathcal S$, then~so~are~$A$~and~$\barA$.
-% \end{block}
-
-% \uncover<3>{
-% \begin{alertblock}{Note}
-% The theorem is no longer true if $\barA$ is replaced by an
-% arbitrary set~$B$.
-% \end{alertblock}
-% }
-% \end{column}
-% \end{columns}
-%}
-
-
-\frame
-{
- \begin{columns}
- \begin{column}{4cm}
- \begin{pgfpicture}{-2cm}{-1.75cm}{2cm}{2.25cm}
- \color{shaded}
- \pgfrect[fill]{\pgfxy(-2,-1.75)}{\pgfxy(4,4)}
- %\pgfcircle[fill]{\pgforigin}{2cm}
-
- \only<1>{%
- \color{white}%
- \pgfcircle[fill]{\pgfpolar{90}{1cm}}{\innerradius}
- \pgfcircle[fill]{\pgfpolar{210}{1cm}}{\innerradius}
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- \pgfclip
-
- \begin{pgftranslate}{\pgfpolar{30}{1cm}}
- \color{softgb}
- \pgfcircle[fill]{\pgfpolar{330}{1cm}}{\radius}
- \end{pgftranslate}
- \end{pgftranslate}}%
- %
- \color{black}
- \pgfcircle[stroke]{\pgfpolar{90}{1cm}}{\innerradius}
- \pgfcircle[stroke]{\pgfpolar{210}{1cm}}{\innerradius}
- \pgfcircle[stroke]{\pgfpolar{330}{1cm}}{\innerradius}
-
- \pgfputat{\pgfrelative{\pgfpolar{90}{1cm}}%
- {\pgfpoint{0pt}{-.5ex}}}%
- {\pgfbox[center,base]{$A\times \barA$}}
- \pgfputat{\pgfrelative{\pgfpolar{210}{1cm}}%
- {\pgfpoint{0pt}{-.5ex}}}%
- {\pgfbox[center,base]{$A\times A$}}
- \pgfputat{\pgfrelative{\pgfpolar{330}{1cm}}%
- {\pgfpoint{0pt}{-.5ex}}}%
- {\pgfbox[center,base]{$\barA\times \barA$}}
-
- \end{pgfpicture}
- \end{column}
- \begin{column}{6.8cm}
- \begin{theorem}
- Let $\mathcal S$ be a well-orderable logical structure in which
- all finite relations are elementarily definable.\\[0.5em]
- If there exist elementarily definable supersets of
- {\color<2>{darkgreen}$A \times A$},
- {\color<2>{darkred}$A \times \barA$}, and
- {\color<2>{darkblue}$\barA \times \barA$} whose
- intersection is empty,\\
- then $A$ is elementarily definable in~$\mathcal S$.
- \end{theorem}
- \begin{alertblock}{Note}<3>
- The theorem is no longer true\\
- if we add $\barA \times A$ to the list.
- \end{alertblock}%
- \end{column}
- \end{columns}
-}
-
-
-\section*{Summary}
-
-\frame
-{
- \frametitle{Summary}
-
- \begin{block}{Summary}
- \begin{itemize}
- \item
- The weak cardinality theorems for first-order logic \alert{unify}\\
- the weak cardinality theorems of automata and recursion theory.
- \item
- The logical approach yields
- weak cardinality theorems for\\ \alert{other computational models}.
- \item
- Cardinality theorems are \alert{separability theorems} in disguise.
- \end{itemize}
- \end{block}{}
-
- \begin{block}{Open Problems}
- \begin{itemize}
- \item
- Does a cardinality theorem for first-order logic hold?
- \item
- What about non-well-orderable structures like $(\mathbb R, +,
- \cdot)$?
- \end{itemize}
- \end{block}
-}
-
-\end{document}
-
-
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--- tetex-src/trunk/source/latex/beamer/lyx/examples/beamerlyxexample1.lyx 2006-10-09 20:57:52 UTC (rev 1756)
+++ tetex-src/trunk/source/latex/beamer/lyx/examples/beamerlyxexample1.lyx 2006-10-09 21:00:50 UTC (rev 1757)
@@ -1,3880 +0,0 @@
-#LyX 1.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 221
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-
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-\begin_inset Formula $t$
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-.
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-
-
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-\layout Corollary
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-In tournaments, paths can be constructed in logarithmic space.
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-\hfill
-
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-Summary
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-Summary
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-
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-
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-\layout Itemize
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-Tournament
-\color red
-reachability
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-\color red
-
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-
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-.
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-There exists a
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-Finding
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-\color red
-
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-
-The same results apply to graphs with
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-\hfill
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-
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-For Further Reading
-\layout BeginFrame
-
-For Further Reading
-\layout Standard
-
-
-\begin_inset ERT
-status Inlined
-
-\layout Standard
-
-\backslash
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-
-
-\layout Bibliography
-\bibitem {Moon1968}
-
-\SpecialChar ~
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-
-\begin_inset ERT
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-
-\backslash
-newblock
-\end_inset
-
-
-\emph on
-Topics on Tournaments.
-
-\emph default
-
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-
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-
-\backslash
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- Holt, Rinehart, and Winston, 1968.
-
-\begin_inset ERT
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-
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-
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-\end_inset
-
-
-\layout Bibliography
-\bibitem {NickelsenT2002}
-
-\SpecialChar ~
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-
-\begin_inset ERT
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-\begin_inset ERT
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-
- In
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-, Springer-Verlag, 2002.
-\layout Bibliography
-\bibitem {Tantau2004b}
-
-\SpecialChar ~
-Till Tantau
-\begin_inset ERT
-status Collapsed
-
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-
-\backslash
-newblock
-\end_inset
-
- A logspace approximation scheme for the shortest path problem for graphs
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-\begin_inset ERT
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-
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-
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-
- In
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-, Springer-Verlag, 2004.
-
-\begin_inset ERT
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-
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- In press.
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-
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-
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-
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-
-Appendix
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-Graphs With Bounded Independence Number
-\layout BeginFrame
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-
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-[label=independence]
-\end_inset
-
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-\layout Definition
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-
-\begin_inset Formula $\alpha(G)$
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-\layout Example
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-
-\layout BeginFrame
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-\layout Theorem
-
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-
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-,
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-
-\begin_inset Formula $k$
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-.
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-
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-
-\begin_inset Formula $k$
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-, there exists a
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-
-\begin_inset Formula $k$
-\end_inset
-
-
-\layout Separator
-
-\layout Theorem
-
-For each\SpecialChar ~
-
-\begin_inset Formula $k$
-\end_inset
-
-, finding the
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-
-\begin_inset Formula $k$
-\end_inset
-
- is
-\color red
-
-\begin_inset Formula $\Class{NL}$
-\end_inset
-
--complete
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-.
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-
-Finding Paths in Undirected Graphs
-\layout BeginFrame
-
-
-\begin_inset ERT
-status Inlined
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-<1-2>[label=undirected]
-\end_inset
-
-The Complexity of Finding Paths in Undirected Graphs
-\newline
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-\layout Fact
-
-
-\begin_inset Formula $\Lang{reach}_{\operatorname{undirected}}$
-\end_inset
-
- is
-\begin_inset Formula $\Class{SL}$
-\end_inset
-
--complete.
-\layout Corollary
-
-For undirected graphs, we can solve
-\begin_deeper
-\layout Itemize
-
-the reachability problem in logspace iff
-\begin_inset Formula $\Class L=\Class{SL}$
-\end_inset
-
-,
-\layout Itemize
-
-the construction problem in logspace iff
-\begin_inset ERT
-status Inlined
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-
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-
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-
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-
-
-\begin_inset ERT
-status Inlined
-
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-[label=optimality]
-\end_inset
-
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-\layout Theorem
-
-Suppose there exists an approximation scheme for
-\begin_inset Formula $\Lang{tournament-shortest-path}$
-\end_inset
-
- that needs space
-\begin_inset Formula $O\bigl(\log|V|\log^{1-\epsilon}\frac{1}{r-1}\bigr)$
-\end_inset
-
-.
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-\begin_inset Formula $\Class{NL}\subseteq\Class{DSPACE}\bigl[\log^{2-\epsilon}n\bigr]$
-\end_inset
-
-.
-\layout Proof
-
-\begin_deeper
-\layout Enumerate
-
-Suppose the approximation scheme exists.
-\newline
-We show
-\begin_inset Formula $\Lang{distance}_{\operatorname{tourn}}\in\Class{DSPACE}\bigl[\log^{2-\epsilon}n\bigr]$
-\end_inset
-
-.
-
-\layout Enumerate
-
-Let
-\begin_inset Formula $(T,s,t)$
-\end_inset
-
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- Let
-\begin_inset Formula $n$
-\end_inset
-
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-\layout Enumerate
-
-Run the approximation scheme for
-\begin_inset Formula $r:=1+\smash{\frac{1}{n+1}}$
-\end_inset
-
-.
-\newline
-This needs space
-\begin_inset Formula $\smash{O(\log^{2-\epsilon}n)}$
-\end_inset
-
-.
-\layout Enumerate
-
-The resulting path has optimal length.
-
-\begin_inset ERT
-status Collapsed
-
-\layout Standard
-
-\backslash
-qedhere
-\end_inset
-
-
-\end_deeper
-\layout EndFrame
-
-\the_end
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