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2019 | OriginalPaper | Buchkapitel

How Petri Net Theory Serves Petri Net Model Checking: A Survey

verfasst von : Karsten Wolf

Erschienen in: Transactions on Petri Nets and Other Models of Concurrency XIV

Verlag: Springer Berlin Heidelberg

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Abstract

Structure theory is a unique treasure of the Petri net community. It was originally studied as a set of stand-alone techniques for exploring Petri net properties such as liveness, boundedness, reachability, and deadlock freedom. Today, methods based on the exploration of the reachability graph (state space methods) dominate Petri net verification. Thanks to the concept of model checking, these methods can deal with a much larger range of verification problems, and thanks to state space reduction methods (symmetries, partial order reduction, and other abstraction techniques), they became tractable for many practical applications. However, in the course of pushing model checking technology to its limits, several elements of Petri net structure theory celebrate a resurrection, being viewed from a different angle. This time, they are used for acceleration of the state space methods. In this article, we give an overview on the use of structural methods in Petri net model checking. We further report on our experience with combining state space and structural methods.

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Fußnoten
1
Stubborn set methods are a class of state space reduction methods. In every marking m, they explore only a subset (“stubborn set”) of the enabled transitions. The stubborn sets are selected such that a given property is preserved (holds in the reduced state space if and only it holds in the full state space). The surveys [52, 53] present stubborn sets in full breadth.
 
Literatur
3.
Zurück zum Zitat Bryant, R.E.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput. Surv. 24(3), 293–318 (1992)MathSciNetCrossRef Bryant, R.E.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput. Surv. 24(3), 293–318 (1992)MathSciNetCrossRef
4.
Zurück zum Zitat Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Congress on Logic, Method, and Philosophy of Science, pp. 1–12 (1962) Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Congress on Logic, Method, and Philosophy of Science, pp. 1–12 (1962)
5.
Zurück zum Zitat Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 10\(^{20}\) states and beyond. In: Proceedings of the LICS, pp. 428–439. IEEE (1990) Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 10\(^{20}\) states and beyond. In: Proceedings of the LICS, pp. 428–439. IEEE (1990)
7.
Zurück zum Zitat Clarke, E.M., Biere, A., Raimi, R., Zhu, Y.: Bounded model checking using satisfiability solving. Formal Methods Syst. Des. 19(1), 7–34 (2001)CrossRef Clarke, E.M., Biere, A., Raimi, R., Zhu, Y.: Bounded model checking using satisfiability solving. Formal Methods Syst. Des. 19(1), 7–34 (2001)CrossRef
8.
Zurück zum Zitat Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)CrossRef Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)CrossRef
9.
Zurück zum Zitat Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked directed graphs. J. Comput. Syst. Sci. 5(5), 511–523 (1971)MathSciNetCrossRef Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked directed graphs. J. Comput. Syst. Sci. 5(5), 511–523 (1971)MathSciNetCrossRef
10.
Zurück zum Zitat Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158 (1971) Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)
11.
Zurück zum Zitat Emerson, E.A., Clarke, E.M.: Using branching time temporal logic to synthesize synchronization skeletons. Sci. Comput. Program. 2(3), 241–266 (1982)CrossRef Emerson, E.A., Clarke, E.M.: Using branching time temporal logic to synthesize synchronization skeletons. Sci. Comput. Program. 2(3), 241–266 (1982)CrossRef
14.
Zurück zum Zitat Evangelista, S., Kristensen, L.M.: A sweep-line method for Büchi automata-based model checking. Fundam. Inform. 131(1), 27–53 (2014)MATH Evangelista, S., Kristensen, L.M.: A sweep-line method for Büchi automata-based model checking. Fundam. Inform. 131(1), 27–53 (2014)MATH
16.
17.
Zurück zum Zitat Hack, M.: Analysis of production schemata by Petri nets. Technical report, MS thesis, Department of Electrical Engineering, MIT, Cambridge, Massachusetts (1972) Hack, M.: Analysis of production schemata by Petri nets. Technical report, MS thesis, Department of Electrical Engineering, MIT, Cambridge, Massachusetts (1972)
18.
Zurück zum Zitat Hack, M.: Decidability questions for Petri nets. Outstanding Dissertations in the Computer Sciences. Garland Publishing, New York (1975) Hack, M.: Decidability questions for Petri nets. Outstanding Dissertations in the Computer Sciences. Garland Publishing, New York (1975)
20.
21.
Zurück zum Zitat Holt, A.W., Commoner, F.: Events and conditions. In: MAC Conference on Concurrent Systems and Parallel Computation, pp. 3–52 (1970) Holt, A.W., Commoner, F.: Events and conditions. In: MAC Conference on Concurrent Systems and Parallel Computation, pp. 3–52 (1970)
22.
Zurück zum Zitat Jensen, K.: Condensed state spaces for symmetrical coloured Petri nets. Formal Methods Syst. Des. 9(1/2), 7–40 (1996)CrossRef Jensen, K.: Condensed state spaces for symmetrical coloured Petri nets. Formal Methods Syst. Des. 9(1/2), 7–40 (1996)CrossRef
23.
Zurück zum Zitat Kam, T., Villa, T., Brayton, R.K.: Multi-valued decision diagrams: theory and applications. Multiple-Valued Logic 4(01), 9–62 (1998)MathSciNetMATH Kam, T., Villa, T., Brayton, R.K.: Multi-valued decision diagrams: theory and applications. Multiple-Valued Logic 4(01), 9–62 (1998)MathSciNetMATH
24.
26.
Zurück zum Zitat Kosaraju, S.R.: Decidability of reachability on vector addition systems. In: ACM Symposium on Theory Computing, pp. 267–281 (1982) Kosaraju, S.R.: Decidability of reachability on vector addition systems. In: ACM Symposium on Theory Computing, pp. 267–281 (1982)
28.
Zurück zum Zitat Lautenbach, K., Schmid, H.A.: Use of Petri nets for proving correctness of concurrent process systems. In: IFIP Congress, pp. 187–191 (1974) Lautenbach, K., Schmid, H.A.: Use of Petri nets for proving correctness of concurrent process systems. In: IFIP Congress, pp. 187–191 (1974)
29.
Zurück zum Zitat Leroux, J.: The general vector addition system reachability problem by Presburger inductive invariants. In: Proceedings of the LICS, pp. 4–13. IEEE (2009) Leroux, J.: The general vector addition system reachability problem by Presburger inductive invariants. In: Proceedings of the LICS, pp. 4–13. IEEE (2009)
30.
Zurück zum Zitat Lipton, R.J.: The reachability problem requires exponential space. Technical report 62, Department of Computer Science, Yale University (1976) Lipton, R.J.: The reachability problem requires exponential space. Technical report 62, Department of Computer Science, Yale University (1976)
32.
Zurück zum Zitat Mayr, E.W.: An algroithm for the general Petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)MathSciNetCrossRef Mayr, E.W.: An algroithm for the general Petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)MathSciNetCrossRef
40.
Zurück zum Zitat Ridder, H.: Analyse von Petri-Netz-Modellen mit Entscheidungsdiagrammen. Ph.D. thesis, Koblenz, Landau, University (1997) Ridder, H.: Analyse von Petri-Netz-Modellen mit Entscheidungsdiagrammen. Ph.D. thesis, Koblenz, Landau, University (1997)
41.
Zurück zum Zitat Roch, S., Starke, P.H.: INA: integrated net analyzer (1999) Roch, S., Starke, P.H.: INA: integrated net analyzer (1999)
45.
Zurück zum Zitat Schmidt, K.: Automated generation of a progress measure for the sweep-line method. STTT 8(3), 195–203 (2006)CrossRef Schmidt, K.: Automated generation of a progress measure for the sweep-line method. STTT 8(3), 195–203 (2006)CrossRef
46.
Zurück zum Zitat Starke, P.H.: Reachability analysis of Petri nets using symmetries. Syst. Anal. Model. Simul. 8(4–5), 293–303 (1991)MathSciNetMATH Starke, P.H.: Reachability analysis of Petri nets using symmetries. Syst. Anal. Model. Simul. 8(4–5), 293–303 (1991)MathSciNetMATH
47.
Zurück zum Zitat Strehl, K., Thiele, L.: Interval diagram techniques for symbolic model checking of Petri nets. In: Proceedings of the Design, Automation and Test in Europe, pp. 756–757 (1999) Strehl, K., Thiele, L.: Interval diagram techniques for symbolic model checking of Petri nets. In: Proceedings of the Design, Automation and Test in Europe, pp. 756–757 (1999)
48.
49.
50.
Zurück zum Zitat Triebel, M., Sürmeli, J.: Characterizing stable and deriving valid inequalities of Petri nets. Fundam. Inform. 146(1), 1–34 (2016)MathSciNetCrossRef Triebel, M., Sürmeli, J.: Characterizing stable and deriving valid inequalities of Petri nets. Fundam. Inform. 146(1), 1–34 (2016)MathSciNetCrossRef
54.
Zurück zum Zitat Vardi, M.Y.: Verification of concurrent programs: the automata-theoretic framework. In: Proceedings of the LICS, pp. 167–176. IEEE (1987) Vardi, M.Y.: Verification of concurrent programs: the automata-theoretic framework. In: Proceedings of the LICS, pp. 167–176. IEEE (1987)
56.
Zurück zum Zitat Wimmel, H., Wolf, K.: Applying CEGAR to the Petri net state equation. Log. Methods Comput. Sci. 8(3) (2012) Wimmel, H., Wolf, K.: Applying CEGAR to the Petri net state equation. Log. Methods Comput. Sci. 8(3) (2012)
58.
Zurück zum Zitat Wolf, K.: A simple abstract interpretation for Petri net queries. In: Proceedings of the PNSE, CEUR Workshop Proceedings, vol. 2138, pp. 163–170 (2018) Wolf, K.: A simple abstract interpretation for Petri net queries. In: Proceedings of the PNSE, CEUR Workshop Proceedings, vol. 2138, pp. 163–170 (2018)
Metadaten
Titel
How Petri Net Theory Serves Petri Net Model Checking: A Survey
verfasst von
Karsten Wolf
Copyright-Jahr
2019
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-60651-3_2