Abstract
The invention of Petri nets was based on a critical analysis of then dominating automata models of systems. Explicit model checking explores the reachable states of a Petri net one by one. Essentially, it transforms a Petri net back to a transition system, that is, an automata-like model. At first glance, this transformation appears to give up on all the specifics of Petri nets. Surveying the most dominant techniques of explicit state space verification, we will, however, work out that even in explicit model checking, the defining features of Petri nets are beneficial and lead to more efficient exploration routines. The findings in this paper are based on practical experience with a Petri net-based explicit model checking tool.
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Bengtsson, J., Larsen, K.G., Larsson, F., Pettersson, P., Wang, Y.: Uppaal–a tool suite for automatic verification of real-time systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) Hybrid Systems. Lecture Notes in Computer Science, vol. 1066, pp. 232–243. Springer (1995)
Christensen, S., Kristensen, L.M., Mailund, T.: A sweep-line method for state space exploration. In: Margaria, T., Wang, Y. (eds.) TACAS. Lecture Notes in Computer Science, vol. 2031, pp. 450–464. Springer, UK (2001)
Commoner, F.: Deadlocks in Petri nets. Applied Data Research Inc, Wakefield, Massachusetts, Report CA-7206-2311 (1972)
Das, D., Chakrabarti, P.P., Kumar, R.: Functional verification of task partitioning for multiprocessor embedded systems. ACM Trans. Des. Autom. Electron. Syst. 12(4) (2007). doi:10.1145/1278349.1278357
Desel, J., Reisig, W.: The synthesis problem of Petri nets. Acta Inf. 33(4), 297–315 (1996)
Ehrenfeucht, A., Rozenberg, G.: Theory of 2-structures, part i: clans, basic subclasses, and morphisms. Theor. Comput. Sci. 70(3), 277–303 (1990)
Fahland, D., Favre, C., Koehler, J., Lohmann, N., Völzer, H., Wolf, K.: Analysis on demand: instantaneous soundness checking of industrial business process models. Data Knowl. Eng. 70(5), 448–466 (2011)
Godefroid, P., Wolper, P.: Using partial orders for the efficient verification of deadlock freedom and safety properties. In: Larsen, K.G., Skou, A. (eds.) CAV. Lecture Notes in Computer Science, vol. 575, pp. 332–342. Springer (1991)
Hack, M.H.T.: Analysis of production schemata by Petri nets. Master’s thesis, MIT, Department of Electrical Engineering, Cambridge, Mass (1972)
Heljanko, K., Esparza, J.: Unfoldings—A Partial-Order Approach to Model Checking. Springer, Berlin (2008)
Huber, P., Jensen, A.M., Jepsen, L.O., Jensen, K.: Towards reachability trees for high-level petri nets. In: Rozenberg, G., Genrich, H.J., Roucairol, G. (eds.) European Workshop on Applications and Theory in Petri Nets. Lecture Notes in Computer Science, vol. 188, pp. 215–233. Springer (1984)
Norris, C., Dill, D.L.: Better verification through symmetry. Form. Methods Syst. Des. 9(1/2), 41–75 (1996)
Kaiser, A., Kroening, D., Wahl, T.: Dynamic cutoff detection in parameterized concurrent programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV. Lecture Notes in Computer Science, vol. 6174, pp. 645–659. Springer (2010)
Kordon, F., Linard, A., Buchs, D., Colange, M., Evangelista, S., Lampka, K., Lohmann, N., Paviot-Adet, E., Thierry-Mieg, Y., Wimmel, H.: Report on the model checking contest at Petri nets 2011. T. Petri nets and other models of concurrency 6, 169–196 (2012)
Kristensen, L.M., Mailund, T.: A generalised sweep-line method for safety properties. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME. Lecture Notes in Computer Science, vol. 2391, pp. 549–567. Springer (2002)
Mayr, E.W.: An algorithm for the general petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)
Nüttgens, M., Feld, T., Zimmermann, V.: Business process modeling with epc and uml: Transformation or integration? pp. 250–261. In: UML, Workshop (1997)
Peled, D.: All from one, one for all: on model checking using representatives. In: Courcoubetis, C. (eds.) Computer Aided Verification: Proceedings of 5th International Conference, CAV ‘93 Elounda, Greece, June 28–July 1. LectureNotes in Computer Science, vol. 697. Springer, Berlin, Heidelberg, pp. 409–423
Petri, C. A.: Kommunikation mit Automaten. In PhD thesis, Technische Universitat Darmstadt, Germany (1962)
Schmidt, K.: How to calculate symmetries of petri nets. Acta Inf. 36(7), 545–590 (2000)
Schmidt, K.: Integrating low level symmetries into reachability analysis. In: Graf, S., Schwartzbach, M.I. (eds.) TACAS. Lecture Notes in Computer Science, vol. 1785, pp. 315–330. Springer (2000)
Schmidt, K.: Explicit State Space Verification. Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Berlin, Germany, Dec, Habilitationsschrift (2002)
Schmidt, K.: Automated generation of a progress measure for the sweep-line method. STTT 8(3), 195–203 (2006)
Stahl, C., Reisig, W., Krstic, M.: Hazard detection in a GALS wrapper: a case study. In: Desel, J., Watanabe, Y. (eds.) Proceedings of the Fifth International Conference on Application of Concurrency to System Design (ACSD’05), pp. 234–243. IEEE Computer Society, St. Malo, France (June 2005)
Stern, U., Dill, D.L.: Parallelizing the mur\(\varphi \) verifier. In: Grumberg, O. (ed.) CAV, vol. 1254 of Lecture Notes in Computer Science, pp. 256–278. Springer (1997)
Talcott, C., Dill, D.L.: The pathway logic assistant. In: Third International Workshop on Computational Methods in, Systems Biology, pp. 228–239 (2005)
Valmari, A.: Stubborn sets for reduced state space generation. In Rozenberg, G. (ed.) Applications and Theory of Petri Nets, vol. 483 of Lecture Notes in Computer Science, pp. 491–515. Springer (1989)
Valmari, A.: The state explosion problem. In Reisig, W., Rozenberg, G. (eds.) Petri Nets, vol. 1491 of Lecture Notes in Computer Science, pp. 429–528. Springer (1996)
Verbeek, H.M.W., van der Aalst, W.M.P.: Woflan 2.0: A Petri-net-based workflow diagnosis tool. In: ICATPN, pp. 475–484 (2000)
Wolf, K.: Generating Petri net state spaces. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN. Lecture Notes in Computer Science, vol. 4546, pp. 29–42. Springer (2007)
Wolper, P., Leroy, D.: Reliable hashing without collision detection. In: Courcoubetis, C. (eds.) Computer Aided Verification: Proceedings of 5th International Conference, CAV ‘93 Elounda, Greece, June 28–July 1. LectureNotes in Computer Science, vol. 697. Springer, Berlin, Heidelberg, pp. 59–70
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Communicated by Dr. Wolfgang Reisig.
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Wolf, K. The Petri net twist in explicit model checking. Softw Syst Model 14, 711–717 (2015). https://doi.org/10.1007/s10270-014-0422-4
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DOI: https://doi.org/10.1007/s10270-014-0422-4