A formal presentation of automaton and Myhill-Nerrode theorem added to serve as a basis for further discussion
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\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,decorations,fit,calc}
\usetikzlibrary{shapes,shapes.arrows,snakes,positioning}
\usepgflibrary{shapes.misc} % LATEX and plain TEX and pure pgf
\usetikzlibrary{matrix}
\usepackage{subfigure}
%\usepackage[pdftex]{hyperref}
% further packages required for unusual symbols (see also
% isabellesym.sty), use only when needed
%\usepackage{amssymb}
%for \<leadsto>, \<box>, \<diamond>, \<sqsupset>, \<mho>, \<Join>,
%\<lhd>, \<lesssim>, \<greatersim>, \<lessapprox>, \<greaterapprox>,
%\<triangleq>, \<yen>, \<lozenge>
%\usepackage[greek,english]{babel}
%option greek for \<euro>
%option english (default language) for \<guillemotleft>, \<guillemotright>
%\usepackage[latin1]{inputenc}
%for \<onesuperior>, \<onequarter>, \<twosuperior>, \<onehalf>,
%\<threesuperior>, \<threequarters>, \<degree>
\usepackage{stmaryrd}
%for \<Sqinter>
%\usepackage{eufrak}
%for \<AA> ... \<ZZ>, \<aa> ... \<zz> (also included in amssymb)
%\usepackage{textcomp}
%for \<cent>, \<currency>
% this should be the last package used
\usepackage{pdfsetup}
% urls in roman style, theory text in math-similar italics
\urlstyle{rm}
\isabellestyle{it}
% for uniform font size
%\renewcommand{\isastyle}{\isastyleminor}
{\theoremstyle{break} \newtheorem{Lem}{Lemma}}
\newcommand{\dfa}[1]{\hat{\delta}_{#1}}
\newcommand{\Lang}{\mathcal{L}}
\newcommand{\mht}{Myhill-Nerode Theorem}
\newcommand{\qnt}[2]{{#1}//{#2}}
\newcommand{\cls}[2]{\llbracket{#1}\rrbracket_{#2}}
\begin{document}
\title{tphols-2011}
\author{By xingyuan}
\maketitle
\tableofcontents
% sane default for proof documents
\parindent 0pt\parskip 0.5ex
% generated text of all theories
\input{session}
% optional bibliography
%\bibliographystyle{abbrv}
%\bibliography{root}
\end{document}
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