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.
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Bonsangue, M.M., Rutten, J.J.M.M., Silva, A.: An algebra for Kripke polynomial coalgebras. In: LICS, pp. 49–58. IEEE Computer Society, Los Alamitos (2009)
Bonsangue, M., Rutten, J., Silva, A.: A Kleene theorem for polynomial coalgebras. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 122–136. Springer, Heidelberg (2009)
Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.L. (eds.): All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)
Goguen, J., Lin, K., Rosu, G.: Circular coinductive rewriting. In: ASE 2000: Proceedings of the 15th IEEE International Conference on Automated Software Engineering, Washington, DC, USA, 2000, pp. 123–132. IEEE Computer Society, Los Alamitos (2000)
Goguen, J.A.: Order-sorted algebra i: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105, 217–273 (1992)
Goriac, E.-I., Lucanu, D., Roşu, G.: Automating Coinduction with Case Analysis. Technical Report TR 10-05, “Al.I.Cuza” University of Iaşi, Faculty of Computer Science (2010), http://www.infoiasi.ro/~tr/tr.pl.cgi
Jacobs, B.: Introduction to coalgebra. towards mathematics of states and observations (2005)
Kleene, S.: Representation of events in nerve nets and finite automata. Automata Studies, 3–42 (1956)
Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. In: LICS, pp. 214–225. IEEE Computer Society, Los Alamitos (1991)
Kozen, D.: Myhill-nerode relations on automatic systems and the completeness of Kleene algebra. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 27–38. Springer, Heidelberg (2001)
Lucanu, D., Goriac, E.-I., Caltais, G., Roşu, G.: CIRC: A behavioral verification tool based on circular coinduction. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 433–442. Springer, Heidelberg (2009)
Roşu, G., Lucanu, D.: Circular Coinduction – A Proof Theoretical Foundation. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 127–144. Springer, Heidelberg (2009)
Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)
Salomaa, A.: Two complete axiom systems for the algebra of regular events. J. ACM 13(1), 158–169 (1966)
Silva, A., Bonsangue, M.M., Rutten, J.J.M.M.: Non-deterministic kleene coalgebras. Logical Methods in Computer Science 6(3) (2010)
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Bonsangue, M., Caltais, G., Goriac, EI., Lucanu, D., Rutten, J., Silva, A. (2011). A Decision Procedure for Bisimilarity of Generalized Regular Expressions. In: Davies, J., Silva, L., Simao, A. (eds) Formal Methods: Foundations and Applications. SBMF 2010. Lecture Notes in Computer Science, vol 6527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19829-8_15
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DOI: https://doi.org/10.1007/978-3-642-19829-8_15
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