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Expressiveness modulo bisimilarity of regular expressions with parallel composition

Published online by Cambridge University Press:  02 January 2015

JOS C. M. BAETEN ,
BAS LUTTIK ,
TIM MULLER  and
PAUL VAN TILBURG
JOS C. M. BAETEN
Affiliation:
CWI, P.O. Box 94079, NL-1090 GB, the Netherlands Email: Jos.Baeten@cwi.nl Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, the Netherlands Email: s.p.luttik@tue.nl, paul@luon.net
BAS LUTTIK
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, the Netherlands Email: s.p.luttik@tue.nl, paul@luon.net Department of Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081, NL-1081 HV Amsterdam, the Netherlands
TIM MULLER
Affiliation:
Faculty of Science, Technology and Communication, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg Email: tim.muller@uni.lu
PAUL VAN TILBURG
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, the Netherlands Email: s.p.luttik@tue.nl, paul@luon.net
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Abstract

The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove that adding pure interleaving to the theory of regular expressions strictly increases its expressiveness modulo bisimilarity. Then, we prove that replacing the operation for pure interleaving by ACP-style parallel composition gives a further increase in expressiveness, still insufficient, however, to facilitate the expression of all finite automata up to bisimilarity. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata up to bisimilarity. Our results extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene's star operation.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Special Issue 6: Special Issue: Express'10 , September 2016 , pp. 933 - 968
Copyright
Copyright © Cambridge University Press 2015 

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