diff -r dae7501b26ac -r 8ce9a432680b Journal/document/root.tex --- a/Journal/document/root.tex Fri Apr 20 14:15:36 2012 +0000 +++ b/Journal/document/root.tex Mon Apr 23 08:01:37 2012 +0000 @@ -1,4 +1,4 @@ -\documentclass[acmtocl]{acmtrans2m} +\documentclass[acmtocl,final]{acmtrans2m} \usepackage{isabelle} \usepackage{isabellesym} \usepackage{amsmath} @@ -9,7 +9,7 @@ \usetikzlibrary{shapes,shapes.arrows,snakes,positioning} \usepgflibrary{shapes.misc} % LATEX and plain TEX and pure pgf \usetikzlibrary{matrix} -%%\usepackage{pdfsetup} +%%%\usepackage{pdfsetup} \usepackage{ot1patch} \usepackage{times} \usepackage{stmaryrd} @@ -48,22 +48,21 @@ Xingyuan Zhang\\PLA University of Science and Technology Nanjing, China \and Christian Urban\\ King's College London, United Kingdom} +\markboth{C.~Wu et al.}{A Formalisation of the Myhill-Nerode Theorem based on Regular + Expressions} + \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 not so straightforward to -formalise in theorem provers. The reason is that a natural -representation for automata are graphs, matrices or functions, none of -which are inductive datatypes. Also convenient operations for disjoint -unions of graphs, matrices and functions are not easily formalisiable -in Isabelle/HOL, the theorem prover we are using. In contrast, regular -expressions can be defined conveniently as a 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. From this theorem many closure properties of regular -languages follow. +There are numerous textbooks on regular languages. Many of them focus +on finite automata for proving properties. Unfortunately, automata +are not so straightforward to formalise in theorem provers. The reason +is that natural representations for automata are graphs, matrices or +functions, none of which are inductive datatypes. Regular +expressions can be defined straightforwardly as a datatype and a +corresponding reasoning infrastructure comes for free in theorem +provers. We show in this paper that a central result from formal +language theory---the Myhill-Nerode Theorem---can be recreated using +only regular expressions. From this theorem many closure properties of +regular languages follow. \end{abstract} \category{F.4.1}{Mathematical Logic and Formal Languages}{Mechanical Theorem Proving} \category{F.4.3}{Mathematical Logic and Formal Languages}{Formal Languages}