A decision procedure for bisimilarity of generalized regular expressions. (English)
Davies, Jim (ed.) et al., Formal methods: foundations and applications. 13th Brazilian symposium on formal methods, SBMF 2010, Natal, Brazil, November 8‒11, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-19828-1/pbk). Lecture Notes in Computer Science 6527, 226-241 (2011).
Summary: 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.