A Decision Procedure for Bisimilarity of Generalized Regular Expressions

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.

[1]  Dexter Kozen.  A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events , 1994, Inf. Comput..

[2]  ALEXANDRA SILVA,et al.  Kleene Coalgebras , 2010 .

[3]  Dexter Kozen,et al.  Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra , 2001, STACS.

[4]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .

[5]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[6]  José Meseguer,et al.  Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations , 1992, Theor. Comput. Sci..

[7]  Grigore Rosu,et al.  CIRC: A Behavioral Verification Tool Based on Circular Coinduction , 2009, CALCO.

[8]  Alexander Kurz,et al.  Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings , 2009, CALCO.

[9]  Alexandra Silva,et al.  An Algebra for Kripke Polynomial Coalgebras , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[10]  Grigore Rosu,et al.  Automating Coinduction with Case Analysis , 2010, ICFEM.

[11]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[12]  Arto Salomaa,et al.  Two Complete Axiom Systems for the Algebra of Regular Events , 1966, JACM.

[13]  José Meseguer,et al.  Specification and proof in membership equational logic , 2000, Theor. Comput. Sci..

[14]  Grigore Rosu,et al.  Circular coinductive rewriting , 2000, Proceedings ASE 2000. Fifteenth IEEE International Conference on Automated Software Engineering.

[15]  Alexandra Silva,et al.  A Kleene Theorem for Polynomial Coalgebras , 2009, FoSSaCS.

[16]  Narciso Martí-Oliet,et al.  All About Maude - A High-Performance Logical Framework, How to Specify, Program and Verify Systems in Rewriting Logic , 2007, All About Maude.

[17]  Alexandra Silva,et al.  Non-Deterministic Kleene Coalgebras , 2010, Log. Methods Comput. Sci..

[18]  Grigore Rosu,et al.  Circular Coinduction: A Proof Theoretical Foundation , 2009, CALCO.