A decision procedure for bisimilarity of generalized regular expressions

Authors:
Marcello Bonsangue;Georgiana Caltais;Eugen-Ioan Goriac;Dorel Lucanu;Jan Rutten;Alexandra Silva
Affiliations:
LIACS - Leiden University, The Netherlands;School of Computer Science - Reykjavik University, Iceland and Faculty of Computer Science - Alexandru Ioan Cuza University, Romania;School of Computer Science - Reykjavik University, Iceland and Faculty of Computer Science - Alexandru Ioan Cuza University, Romania;Faculty of Computer Science - Alexandru Ioan Cuza University, Romania and Radboud University Nijmegen, The Netherlands and Vrije Universiteit Amsterdam, The Netherlands;Centrum voor Wiskunde en Informatica, The Netherlands;Centrum voor Wiskunde en Informatica, The Netherlands
Venue:
SBMF'10 Proceedings of the 13th Brazilian conference on Formal methods: foundations and applications
Year:
2010

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Abstract

A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene's theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata and Mealy machines. In this paper, we present a novel algorithm and a tool to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations.