Abstract
Infinite-state reachability problems arising from unbounded-thread program verification are of great practical importance, yet algorithmically hard. Despite the remarkable success of explicit-state exploration methods to solve such problems, there is a sense that SMT technology can be beneficial to speed up the decision making. This vision was pioneered in recent work by Esparza et al. on SMT-based coverability analysis of Petri nets. We present here an approximate coverability method that operates on thread-transition systems, a model naturally derived from predicate abstractions of multi-threaded programs. In addition to successfully proving uncoverability for all our safe benchmark programs, our approach extends previous work by the ability to decide the unsafety of many unsafe programs, and to provide a witness path. We also demonstrate experimentally that our method beats all leading explicit-state techniques on safe benchmarks and is competitive on unsafe ones, promising to be a very accurate and fast coverability analyzer.
This work is supported by NSF grant no. CCF-1253331.
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Petrinizer offers four methods; we use the most powerful: refinement over integers.
References
Abdulla, P.A., Haziza, F., Holík, L.: All for the price of few (parameterized verification through view abstraction). In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 476–495. Springer, Heidelberg (2013)
Abdulla, P.A.: Well (and better) quasi-ordered transition systems. Bull. Symbolic Logic 16(4), 457–515 (2010)
Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: LICS, pp. 313–321 (1996)
Cardoza, E., Lipton, R.J., Meyer, A.R.: Exponential space complete problems for petri nets and commutative semigroups: preliminary report. In: STOC, pp. 50–54 (1976)
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)
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)
Esparza, J., Meyer, P.J.: An SMT-based approach to fair termination analysis. In: FMCAD, pp. 49–56 (2015)
Even, S.: Graph Algorithms. W. H. Freeman & Co., New York (1979)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Theor. Comput. Sci. 256(1–2), 63–92 (2001)
Ganty, P., Raskin, J.F., Van Begin, L.: From many places to few: automatic abstraction refinement for petri nets. Fundam. Inf. 88(3), 275–305 (2008)
Geeraerts, G., Raskin, J.F., Begin, L.V.: Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS. J. Comput. Syst. Sci. 72(1), 180–203 (2006)
Geeraerts, G., Raskin, J.-F., Van Begin, L.: On the efficient computation of the minimal coverability set for petri nets. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 98–113. Springer, Heidelberg (2007)
German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)
Hajdu, Á., Vörös, A., Bartha, T.: New search strategies for the petri net CEGAR approach. In: Devillers, R., Valmari, A. (eds.) PETRI NETS 2015. LNCS, vol. 9115, pp. 309–328. Springer, Heidelberg (2015)
Kaiser, A., Kroening, D., Wahl, T.: A widening approach to multithreaded program verification. ACM Trans. Program. Lang. Syst. 36(4), 14 (2014)
Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)
Kloos, J., Majumdar, R., Niksic, F., Piskac, R.: Incremental, inductive coverability. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 158–173. Springer, Heidelberg (2013)
Liu, P.: www.ccs.neu.edu/home/lpzun/tse/
Liu, P., Wahl, T.: Infinite-state backward exploration of Boolean broadcast programs. In: FMCAD, pp. 155–162 (2014)
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, 223–231 (1978)
Reynier, P.-A., Servais, F.: Minimal coverability set for petri nets: Karp and Miller algorithm with pruning. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 69–88. Springer, Heidelberg (2011)
Valmari, A., Hansen, H.: Old and new algorithms for minimal coverability sets. In: Haddad, S., Pomello, L. (eds.) PETRI NETS 2012. LNCS, vol. 7347, pp. 208–227. Springer, Heidelberg (2012)
Wimmel, H., Wolf, K.: Applying CEGAR to the petri net state equation. Log. Methods Comput. Sci. 8(3), 827–846 (2012)
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Athanasiou, K., Liu, P., Wahl, T. (2016). Unbounded-Thread Program Verification using Thread-State Equations. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_35
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