Abstract
Parameterised Boolean equation systems (PBESs) can be used for solving a variety of verification problems such as model checking and equivalence checking problems. The definition of solution for a PBES is notoriously difficult to understand, which makes them hard to work with. Tan and Cleaveland proposed a notion of proof for Boolean equation systems they call support sets. We show that an adapted notion of support sets called proof graphs gives an alternative characterisation of the solution to a PBES, and prove that minimising proof graphs is NP-hard. Finally, we explain how proof graphs may be used in practice and illustrate how they can be used in equivalence checking to generate distinguishing formulas.
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References
Chen, T., Ploeger, B., van de Pol, J., Willemse, T.A.C.: Equivalence checking for infinite systems using parameterized boolean equation systems. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 120–135. Springer, Heidelberg (2007)
Clarke, E., Grumberg, O., McMillan, K., Zhao, X.: Efficient generation of counterexamples and witnesses in symbolic model checking. In: DAC 1995, pp. 427–432. ACM (1995)
Clarke, E., Jha, S., Lu, Y., Veith, H.: Tree-like counterexamples in model checking. In: LICS, pp. 19–29. IEEE (2002)
Cranen, S., Groote, J., Reniers, M.: A linear translation from CTL* to the first-order modal μ-calculus. TCS 412, 3129–3139 (2011)
Emerson, E., Jutla, C.: Tree automata, mu-calculus and determinacy. In: FOCS, pp. 368–377. IEEE Computer Society (1991)
Goldsmith, J., Hagen, M., Mundhenk, M.: Complexity of DNF minimization and isomorphism testing for monotone formulas. Information and Computation 206(6), 760–775 (2008)
Groote, J.F., Keinänen, M.: A sub-quadratic algorithm for conjunctive and disjunctive Boolean equation systems. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 532–545. Springer, Heidelberg (2005)
Groote, J., Reniers, M.: Algebraic process verification. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra. Elsevier (2001)
Groote, J.F., Willemse, T.A.C.: Parameterised boolean equation systems (extended abstract). In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 308–324. Springer, Heidelberg (2004)
King, V., Kupferman, O., Vardi, M.Y.: On the complexity of parity word automata. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 276–286. Springer, Heidelberg (2001)
Mateescu, R.: Efficient diagnostic generation for Boolean equation systems. In: Graf, S. (ed.) TACAS 2000. LNCS, vol. 1785, pp. 251–265. Springer, Heidelberg (2000)
Sahni, S.: Computationally related problems. SICOMP 3(4), 262–279 (1974)
Tan, L.: Evidence-Based Verification. PhD thesis, Department of Computer Science, State University of New York (2002)
Tan, L., Cleaveland, W.R.: Evidence-based model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 455–470. Springer, Heidelberg (2002)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. TCS 200(1-2), 135–183 (1998)
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Cranen, S., Luttik, B., Willemse, T.A.C. (2013). Proof Graphs for Parameterised Boolean Equation Systems. In: D’Argenio, P.R., Melgratti, H. (eds) CONCUR 2013 – Concurrency Theory. CONCUR 2013. Lecture Notes in Computer Science, vol 8052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40184-8_33
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DOI: https://doi.org/10.1007/978-3-642-40184-8_33
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