Abstract
Thanks to the development of a number of efficiency enhancing techniques, state-space exploration based verification, and in particular model checking, has been quite successful for finite-state systems. This has prompted efforts to apply a similar approach to systems with infinite state spaces. Doing so amounts to developing algorithms for computing a symbolic representation of the infinite state space, as opposed to requiring the user to characterize the state space by assertions. Of course, in most cases, this can only be done at the cost of forgoing any general guarantee of success. The goal of this paper is to survey a number of results in this area and to show that a surprisingly common characteristic of the systems that can be analyzed with this approach is that their state space can be represented as a regular language.
“Charge de Recherches” (Post-Doctoral Researcher) for the National Fund for Scientific Research (Belgium).
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183–236, 1994.
B. Boigelot, L. Bronne, and S. Rassart. An improved reachability analysis method for strongly linear hybrid systems. In Proc. 9th Int. Conf on Computer Aided Verification, volume 1254 of Lecture Notes in Computer Science, pages 167–178, Haifa, June 1997. Springer-Verlag.
A. Boudet and H. Comon. Diophantine equations, Presburger arithmetic and finite automata. In Proceedings of CAAP'96, number 1059 in Lecture Notes in Computer Science, pages 30–43. Springer-Verlag, 1996.
J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang. Symbolic model checking: 102° states and beyond. Information and Computation, 98(2):142–170, June 1992.
B. Boigelot and P. Godefroid. Symbolic verification of communication protocols with infinite state spaces using QDDs. In Proceedings of Computer-Aided Verification, volume 1102 of Lecture Notes in Computer Science, pages 1–12, New-Brunswick, NJ, USA, July 1996. Springer-Verlag.
B. Boigelot, P. Godefroid, B. Willems, and P. Wolper. The power of QDD's. In Proc. of Int. Static Analysis Symposium, volume 1302 of Lecture Notes in Computer Science, pages 172–186, Paris, September 1997. Springer-Verlag.
B. Boigelot. Symbolic Methods for Exploring Infinite State Spaces. PhD thesis, Université de Liege, 1998.
B. Boigelot, S. Rassart, and P. Wolper. On the expressiveness of real and integer arithmetic automata. to appear in Proc. ICALP'98, 1998.
R.E. Bryant. Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys, 24(3):293–318, 1992.
O. Burkart and B. Steffen. Composition, decomposition and model checking of pushdown processes. Nordic Journal of Computing, 2(2):89–125, 1995.
J. R. Büchi. Weak second-order arithmetic and finite automata. Zeitschrift Math. Logik and Grundlagen der Mathematik, 6:66–92, 1960.
O. Bernholtz, M.Y. Vardi, and P. Wolper. An automata-theoretic approach to branching-time model checking. In Computer Aided Verification, Proc. 6th Int. Workshop, volume 818 of Lecture Notes in Computer Science, pages 142–155, Stanford, California, June 1994. Springer-Verlag. full version available from authors.
B. Boigelot and P. Wolper. Symbolic verification with periodic sets. In Computer Aided Verification, Proc. 6th Int. Conference, volume 818 of Lecture Notes in Computer Science, pages 55–67, Stanford, California, June 1994. Springer-Verlag.
D. Caucal. On the regular structure of prefix rewriting. Theoretical Computer Science, 106:61–86, 1992.
A. Cobham. On the base-dependence of sets of numbers recognizable by finite automata. Mathematical Systems Theory, 3:186–192, 1969.
J. Esparza and M. Nielsen. Decidability issues for Petri nets — a survey. Bulletin of the EATCS, 52:245–262, 1994.
A. Finkel, B. Willems, and P. Wolper. A direct symbolic approach to model checking pushdown systems (extended abstract). Presented at Infinity'97 (Bologna), Electronic notes in theoretical computer science, August 1997.
A. L. Semenov. Presburgerness of predicates regular in two number systems. Siberian Mathematical Journal, 18:289–299, 1977.
A. Valmari. A stubborn attack on state explosion. Formal Methods in System Design, 1:297–322, 1992.
M.Y. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. In Proceedings of the First Symposium on Logic in Computer Science, pages 322–331, Cambridge, June 1986.
P. Wolper and B. Boigelot. An automata-theoretic approach to presburger arithmetic constraints. In Proc. Static Analysis Symposium, volume 983 of Lecture Notes in Computer Science, pages 21–32, Glasgow, September 1995. Springer-Verlag.
P. Wolper and P. Godefroid. Partial-order methods for temporal verification. In Proc. CONCUR '93, volume 715 of Lecture Notes in Computer Science, pages 233–246, Hildesheim, August 1993. Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wolper, P., Boigelot, B. (1998). Verifying systems with infinite but regular state spaces. In: Hu, A.J., Vardi, M.Y. (eds) Computer Aided Verification. CAV 1998. Lecture Notes in Computer Science, vol 1427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028736
Download citation
DOI: https://doi.org/10.1007/BFb0028736
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64608-2
Online ISBN: 978-3-540-69339-0
eBook Packages: Springer Book Archive