Abstract
Current algorithms for the automatic verification of Petri nets suffer from the explosion caused by the high dimensionality of the state spaces of practical examples. In this paper, we develop an abstract interpretation based analysis that reduces the dimensionality of state spaces that are explored during verification. In our approach, the dimensionality is reduced by trying to gather places that may not be important for the property to establish. If the abstraction that is obtained is too coarse, an automatic refinement is performed and a more precise abstraction is obtained. The refinement is computed by taking into account information about the inconclusive analysis. The process is iterated until the property is proved to be true or false.
This research was supported the Belgian FNRS grant 2.4530.02 of the FRFC project “Centre Fédéré en Vérification” and by the project “MoVES”, an Interuniversity Attraction Poles Programme of the Belgian Federal Government.
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References
German, S.M., Sistla, A.P.: Reasoning about Systems with Many Processes. Journal of ACM 39, 675–735 (1992)
Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Comput. Syst. Sci. 3, 147–195 (1969)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere? Theoretical Computer Science 256(2-3), 63–92 (2001)
Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: LICS. Proc. of the 11th Annual IEEE Symp. on Logic in Computer Science, pp. 313–321. IEEE Computer Society Press, Washington (1996)
Delzanno, G., Raskin, J.F., Van Begin, L.: Attacking Symbolic State Explosion. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 298–310. Springer, Heidelberg (2001)
Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric systems. PhD thesis, Université Libre de Bruxelles, Belgium [1] (2003)
Abdulla, P.A., Iyer, S.P., Nylén, A.: Unfoldings of unbounded petri nets. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 495–507. Springer, Heidelberg (2000)
Grahlmann, B.: The PEP Tool. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 440–443. Springer, Heidelberg (1997)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL 77. Proc. 4th ACM SIGACT-SIGPLAN Symp. on Principles of Programming Languages, pp. 238–252. ACM Press, New York (1977)
Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003)
Berthelot, G., Roucairol, G., Valk, R.: Reductions of nets and parallel prgrams. In: Advanced Cource: Net Theory and Applications. LNCS, vol. 84, pp. 277–290. Springer, Heidelberg [3] (1975)
Cousot, P.: Partial completeness of abstract fixpoint checking, invited paper. In: Choueiry, B.Y., Walsh, T. (eds.) SARA 2000. LNCS (LNAI), vol. 1864, pp. 1–25. Springer, Heidelberg [4, 5, 18] (2000)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Amer. J. Math. 35, 413–422 [5] (1913)
Ganty, P., Raskin, J.F., Van Begin, L.: A complete abstract interpretation framework for coverability properties of WSTS. In: VMCAI 2006. LNCS, vol. 3855, pp. 49–64. Springer, Heidelberg [128, 138, 141] (2006)
Geeraerts, G., Raskin, J.F., Van Begin, L.: Expand, enlarge and check: new algorithms for the coverability problem of WSTS. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 287–298. Springer, Heidelberg [5, 15, 18, 19] (2004)
Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra. Springer, New York (1981)
Ganty, P., Meuter, C., Delzanno, G., Kalyon, G., Raskin, J.F., Van Begin, L.: Symbolic data structure for sets of k-uples. Technical report [18] (2007)
Marsan, M.A., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Series in Parallel Computing [18] (1995)
Ciardo, G., Miner, A.: Storage Alternatives for Large Structured State Space. In: Marie, R., Plateau, B., Calzarossa, M.C., Rubino, G.J. (eds.) Computer Performance Evaluation Modelling Techniques and Tools. LNCS, vol. 1245, pp. 44–57. Springer, Heidelberg [18] (1997)
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Ganty, P., Raskin, JF., Van Begin, L. (2007). From Many Places to Few: Automatic Abstraction Refinement for Petri Nets. In: Kleijn, J., Yakovlev, A. (eds) Petri Nets and Other Models of Concurrency – ICATPN 2007. ICATPN 2007. Lecture Notes in Computer Science, vol 4546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73094-1_10
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DOI: https://doi.org/10.1007/978-3-540-73094-1_10
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