| author | urbanc |
| Mon, 05 Sep 2011 12:07:16 +0000 | |
| changeset 233 | e2dc11e12e0b |
| parent 200 | 204856ef5573 |
| child 245 | 40b8d485ce8d |
| permissions | -rw-r--r-- |
| 167 | 1 |
\documentclass{ita}
|
| 24 | 2 |
\usepackage{isabelle}
|
3 |
\usepackage{isabellesym}
|
|
4 |
\usepackage{amsmath}
|
|
5 |
\usepackage{amssymb}
|
|
6 |
\usepackage{tikz}
|
|
7 |
\usepackage{pgf}
|
|
| 125 | 8 |
\usetikzlibrary{arrows,automata,decorations,fit,calc}
|
9 |
\usetikzlibrary{shapes,shapes.arrows,snakes,positioning}
|
|
10 |
\usepgflibrary{shapes.misc} % LATEX and plain TEX and pure pgf
|
|
11 |
\usetikzlibrary{matrix}
|
|
| 24 | 12 |
\usepackage{pdfsetup}
|
13 |
\usepackage{ot1patch}
|
|
14 |
\usepackage{times}
|
|
| 161 | 15 |
%%\usepackage{proof}
|
| 90 | 16 |
%%\usepackage{mathabx}
|
|
52
4a517c6ac07d
tuning of the syntax; needs the stmaryrd latex package
urbanc
parents:
24
diff
changeset
|
17 |
\usepackage{stmaryrd}
|
| 233 | 18 |
\usepackage{mathpartir}
|
| 123 | 19 |
|
| 24 | 20 |
\urlstyle{rm}
|
21 |
\isabellestyle{it}
|
|
22 |
\renewcommand{\isastyleminor}{\it}%
|
|
23 |
\renewcommand{\isastyle}{\normalsize\it}%
|
|
24 |
||
| 174 | 25 |
\newcommand*{\threesim}{%
|
26 |
\mathrel{\vcenter{\offinterlineskip
|
|
27 |
\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}}
|
|
| 24 | 28 |
|
29 |
\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
|
|
30 |
\renewcommand{\isasymequiv}{$\dn$}
|
|
31 |
\renewcommand{\isasymemptyset}{$\varnothing$}
|
|
32 |
\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
|
|
33 |
||
| 83 | 34 |
\newcommand{\isasymcalL}{\ensuremath{\cal{L}}}
|
| 90 | 35 |
\newcommand{\isasymbigplus}{\ensuremath{\bigplus}}
|
36 |
||
| 94 | 37 |
\newcommand{\bigplus}{\mbox{\Large\bf$+$}}
|
| 24 | 38 |
\begin{document}
|
39 |
||
| 172 | 40 |
\title{A Formalisation of the Myhill-Nerode Theorem\\ based on Regular
|
| 167 | 41 |
Expressions} |
| 175 | 42 |
\thanks{This is a revised and expanded version of \cite{WuZhangUrban11}.}
|
| 167 | 43 |
\author{Chunhan Wu}\address{PLA University of Science and Technology, China}
|
44 |
\author{Xingyuan Zhang}\sameaddress{1}
|
|
45 |
\author{Christian Urban}\address{TU Munich,
|
|
|
200
204856ef5573
added an example for non-regularity and continuation lemma (the example does not yet work)
urbanc
parents:
187
diff
changeset
|
46 |
Germany}\secondaddress{corresponding author}
|
| 174 | 47 |
\subjclass{68Q45}
|
48 |
\keywords{Myhill-Nerode theorem, regular expressions, Isabelle theorem prover}
|
|
| 24 | 49 |
|
50 |
\begin{abstract}
|
|
| 88 | 51 |
There are numerous textbooks on regular languages. Nearly all of them |
52 |
introduce the subject by describing finite automata and only mentioning on the |
|
| 115 | 53 |
side a connection with regular expressions. Unfortunately, automata are difficult |
54 |
to formalise in HOL-based theorem provers. The reason is that |
|
| 88 | 55 |
they need to be represented as graphs, matrices or functions, none of which |
56 |
are inductive datatypes. Also convenient operations for disjoint unions of |
|
| 187 | 57 |
graphs, matrices and functions are not easily formalisiable in HOL. In contrast, regular |
| 154 | 58 |
expressions can be defined conveniently as a datatype and a corresponding |
| 88 | 59 |
reasoning infrastructure comes for free. We show in this paper that a central |
60 |
result from formal language theory---the Myhill-Nerode theorem---can be |
|
61 |
recreated using only regular expressions. |
|
| 24 | 62 |
\end{abstract}
|
| 167 | 63 |
\maketitle |
| 75 | 64 |
|
| 24 | 65 |
\input{session}
|
66 |
||
| 154 | 67 |
%%\mbox{}\\[-10mm]
|
| 24 | 68 |
\bibliographystyle{plain}
|
69 |
\bibliography{root}
|
|
70 |
||
71 |
\end{document}
|
|
72 |
||
73 |
%%% Local Variables: |
|
74 |
%%% mode: latex |
|
75 |
%%% TeX-master: t |
|
76 |
%%% End: |