diff -r e31b733ace44 -r f72c82bf59e5 Paper/document/root.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Paper/document/root.tex Thu Nov 25 18:54:45 2010 +0000 @@ -0,0 +1,57 @@ +\documentclass{llncs} +\usepackage{isabelle} +\usepackage{isabellesym} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{tikz} +\usepackage{pgf} +\usepackage{pdfsetup} +\usepackage{ot1patch} +\usepackage{times} +\usepackage{proof} + + +\urlstyle{rm} +\isabellestyle{it} +\renewcommand{\isastyleminor}{\it}% +\renewcommand{\isastyle}{\normalsize\it}% + + +\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,} +\renewcommand{\isasymequiv}{$\dn$} +\renewcommand{\isasymemptyset}{$\varnothing$} +\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}} + +\begin{document} + +\title{A Formalisation of the Myhill-Nerode Theorem\\ based on Regular Expressions} +\author{Chunhan Wu\inst{1} \and Xingjuan Zhang\inst{1} \and Christian Urban\inst{2}} +\institute{PLA University, China \and TU Munich, Germany} +\maketitle + +\begin{abstract} +There are numerous textbooks on regular languages. Nearly all of them +introduce the subject by describing finite automata and +only mentioning on the side a connection with regular expressions. +Unfortunately, automata are a hassle for formalisations in HOL-based +theorem provers. The reason is they need to be represented as graphs +or matrices, neither of which can be easily defined as datatype. Also +operations, such as disjoint union of graphs, are not easily formalisiable +in HOL. In contrast, regular expressions can be defined easily +as datatype and a corresponding reasoning infrastructure comes for +free. We show in this paper that a central result from formal +language theory---the Myhill-Nerode theorem---can be recreated +using only regular expressions. +\end{abstract} + +\input{session} + +\bibliographystyle{plain} +\bibliography{root} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: