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Model checking of persistent Petri nets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

Abstract

In this paper we develop a model checking algorithm which is fast in the size of the system. The class of system models we consider are safe persistent Petri nets; the logic is S 4, i.e. prepositional logic with a ‘some time’ operator. Our algorithm does not require to construct any transition system: We reduce the model checking problem to the problem of computing certain Parikh vectors, and we show that for the class of safe marked graphs these vectors can be computed — from the structure of the Petri net — in polynomial time in the size of the system.

Partly supported by the Esprit Basic Research Action 3148 DEMON.

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References

  1. G.S. Avrunin, U.A. Buy, J.C. Corbett, L.K. Dillon and J.C. Wileden: Automated Analysis of Concurrent Systems with the Constrained Expression Toolset. COINS Technical Report 90–116, University of Massachussets at Amherst (1990).

    Google Scholar 

  2. E. Best and R. Devillers: Sequential and Concurrent Behaviour in Petri Net Theory. TCS Vol. 55, 87–136 (1987).

    Google Scholar 

  3. E. Best and J. Esparza: Model Checking of Persistent Petri Nets. Hildesheimer Informatik Fachbericht 11/91 (1991).

    Google Scholar 

  4. E. Best and C. Fernández: Nonsequential Processes — a Petri Net View. EATCS Monographs on Theoretical Computer Science Vol.13 (1988).

    Google Scholar 

  5. E.M. Clarke, O. Grumberg, M.C. Browne: Reasoning about Networks with many identical finite—state processes. Proceedings of the Fifth Annual Symposium on Principles of Distributed Computing, 240–248 (1986).

    Google Scholar 

  6. J.M. Colom: Structural Analysis Techniques Based on Linear Programming and Convex Geometry. Ph. D. Thesis, University of Zaragoza (1990) (in Spanish).

    Google Scholar 

  7. F. Commoner, A.W. Holt, S. Even and A. Pnueli: Marked Directed Graphs. Journal of Computer and System Science Vol.5, 511–523 (1971).

    Google Scholar 

  8. C. Fernández, M. Nielsen and P.S. Thiagarajan: Notions of Realisable Non-Sequential Processes. Fundamenta Informaticae IX, 421–454 (1986).

    Google Scholar 

  9. P. Godefroid: Using Partial Orders to Improve Automatic Verification Methods. Proc. of Computer-Aided Verification Workshop, Rutgers, New Jersey (1990).

    Google Scholar 

  10. G.E. Hughes and M.J. Creswell: An Introduction to Modal Logic. Methuen and Co. (1968).

    Google Scholar 

  11. R. Janicki and M. Koutny: Optimal Simulation for the Verification of Concurrent Systems. Technical report, McMaster University (1989).

    Google Scholar 

  12. M. Jantzen: Complexity of Place/Transition Nets. Petri Nets: Central Models and Their Properties. W. Brauer, W. Reisig, G. Rozenberg (eds.), LNCS 254, 397–412 (1987).

    Google Scholar 

  13. L.H. Landweber and E.L. Robertson: Properties of Conflict-free and Persistent Petri Nets. JACM Vol.25, No.3, 352–364 (1978).

    Google Scholar 

  14. T. Murata: Petri Nets: Properties, Analysis and Applications. Proc. of the IEEE Vol. 77, No. 4, 541–580 (1989).

    Google Scholar 

  15. H. Qin: Efficient Verification of Determinate Processes. CONCUR'91, J.C.M. Baeten, J.F. Groote (eds.), LNCS 527, 470–479 (1991).

    Google Scholar 

  16. W. Reisig: Petri Nets-an Introduction. EATCS Monographs on Theoretical Computer Science, Vol. 4, Springer Verlag (1985).

    Google Scholar 

  17. M. Tiusanen: Some Unsolved Problems in Modelling Self-timed Circuits Using Petri Nets. EATCS Bulletin, Vol. 36, 152–160 (1988).

    Google Scholar 

  18. A. Valmari: Stubborn Sets for Reduced State Space Generation. Advances in Petri Nets 1990, G. Rozenberg (ed.), LNCS 483, 491–515 (1990).

    Google Scholar 

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Authors

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Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

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© 1992 Springer-Verlag Berlin Heidelberg

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Best, E., Esparza, J. (1992). Model checking of persistent Petri nets. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023756

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  • DOI: https://doi.org/10.1007/BFb0023756

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

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