Abstract
The verification of safety properties for concurrent systems often reduces to the coverability problem for Petri nets. This problem was shown to be ExpSpace-complete forty years ago. Driven by the concurrency revolution, it has regained a lot of interest over the last decade. In this paper, we propose a generic and simple approach to solve this problem. Our method is inspired from the recent approach of Blondin, Finkel, Haase and Haddad [3]. Basically, we combine forward invariant generation techniques for Petri nets with backward reachability for well-structured transition systems. An experimental evaluation demonstrates the efficiency of our approach.
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Notes
- 1.
The statement of Theorem 7 in [18] is wrong since it is based on a too strong definition of limit-reachability. However, the proof becomes correct with our definitions and notations.
References
Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.: Algorithmic analysis of programs with well quasi-ordered domains. Inf. Comput. 160(1–2), 109–127 (2000)
Blondin, M., Finkel, A., Haase, C., Haddad, S.: QCover with benchmarks. http://www-etud.iro.umontreal.ca/~blondimi/doc/qcover_with_benchmarks.zip
Blondin, M., Finkel, A., Haase, C., Haddad, S.: Approaching the coverability problem continuously. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 480–496. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49674-9_28
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252. ACM (1977)
Donaldson, A., Kaiser, A., Kroening, D., Wahl, T.: Symmetry-aware predicate abstraction for shared-variable concurrent programs. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 356–371. Springer, Heidelberg (2011)
D’Osualdo, E., Kochems, J., Ong, C.-H.L.: Automatic verification of Erlang-style concurrency. In: Logozzo, F., Fähndrich, M. (eds.) Static Analysis. LNCS, vol. 7935, pp. 454–476. Springer, Heidelberg (2013)
Esparza, J., Ledesma-Garza, R., Majumdar, R., Meyer, P., Niksic, F.: An SMT-based approach to coverability analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 603–619. Springer, Heidelberg (2014)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Inf. Comput. 256(1–2), 63–92 (2001)
Fraca, E., Haddad, S.: Complexity analysis of continuous Petri nets. Inf. Comput. 137(1), 1–28 (2015)
Ganty, P.: Mist - a safety checker for petri nets and extensions. http://github.com/pierreganty/mist
Geffroy, T., Leroux, J., Sutre, G.: ICover patch. http://dept-info.labri.u-bordeaux.fr/~tgeffroy/icover/
German, S.M., Sistla, A.P.: Reasoning about systems with many processes. Inf. Comput. 39(3), 675–735 (1992)
Kaiser, A., Kroening, D., Wahl, T.: A widening approach to multithreaded program verification. ACM Trans. Program. Lang. Syst. 36(4), 14:1–14:29 (2014)
Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)
Lipton, R.J.: The reachability problem requires exponential space. Technical report 62, Yale University (1976)
de Moura, L., Bjørner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comput. Sci. 6(2), 223–231 (1978)
Recalde, L., Teruel, E., Silva, M.: Autonomous continuous P/T systems. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, pp. 107–126. Springer, Heidelberg (1999)
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Geffroy, T., Leroux, J., Sutre, G. (2016). Occam’s Razor Applied to the Petri Net Coverability Problem. In: Larsen, K., Potapov, I., Srba, J. (eds) Reachability Problems. RP 2016. Lecture Notes in Computer Science(), vol 9899. Springer, Cham. https://doi.org/10.1007/978-3-319-45994-3_6
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