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Petri nets, traces, and local model checking

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 936))

Abstract

It has been observed that the behavioural view of concurrent systems that all possible sequences of actions are relevant is too generous; not all sequences should be considered as likely behaviours. By taking progress fairness assumptions into account one obtains a more realistic behavioural view of the systems. In this paper we consider the problem of performing model checking relative to this behavioural view. We present a CTL-like logic which is interpreted over the model of concurrent systems labelled 1-safe nets. It turns out that Mazurkiewicz trace theory provides a useful setting in which the progress fairness assumptions can be formalized in a natural way. We provide the first, to our knowledge, set of sound and complete tableau rules for a CTL-like logic interpreted under progress fairness assumptions.

This work has been supported by The Danish Research Councils and the Danish Research Academy. Part of this work was done at BRCIS.

Visiting from Aarhus, BRICS, Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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References

  1. M. A. Bednarczyk. Categories of asynchronous systems. PhD thesis, University of Sussex, 1988. PhD in computer science, report no.1/88.

    Google Scholar 

  2. Allan Cheng, Javier Esparza, and Jens Palsberg. Complexity results for 1-safe nets. In Proc. FST&TCS 13, Thirteenth Conference on the Foundations of Software Technology & Theoretical Computer Science, pages 326–337. Springer-Verlag (LNCS 761), Bombay, India, December 1993. To appear in TCS, volume 148.

    Google Scholar 

  3. Edmund M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finite state concurrent system using temporal logic. ACM Transactions on Programming Languages and Systems, 8(2):244–263, 1986.

    Google Scholar 

  4. Allan Cheng. Local Model Checking and Traces. Technical report, Daimi, Computer Science Department, Aarhus University, May 1994. BRICS Report Series RS-94-17.

    Google Scholar 

  5. Allan Cheng. Complexity Results for Model Checking. Research Series RS-95-18, BRICS, Department of Computer Science, University of Aarhus, 1995.

    Google Scholar 

  6. Allan Cheng. Petri Nets, Traces, and Local Model Checking. Research series, BRICS, 1995. Full version of paper to appear in proceedings of AMAST'95. In preparation.

    Google Scholar 

  7. Lalita Jategaonkar and Albert Meyer. Deciding true concurrency equivalences on finite safe nets. In Proc. ICALP'93, pages 519–531, 1993.

    Google Scholar 

  8. André Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation and open maps. In Proc. LICS'93, Eighth Annual Symposium on Logic in Computer Science, pages 418–427, 1993.

    Google Scholar 

  9. Marta Z. Kwiatkowska. Event fairness and non-interleaving concurrency. Formal Aspects of Computing, 1:213–228, 1989.

    Google Scholar 

  10. Kim G. Larsen. Proof systems for Hennessy-Milner logic with recursion. In Proceedings of CAAP, Nancy France, pages 215–230. Springer-Verlag (LNCS 299), March 1988.

    Google Scholar 

  11. Kamal Lodaya, Rohit Parikh, R. Ramanujam, and P. S. Thiagarajan. A logical study of distributed transition systems. Technical report, School of Mathematics, SPIC Science Foundation, Madras, 1993. To appear in Information and Computation, a preliminary version appears as Report TCS-93-8.

    Google Scholar 

  12. Antoni Mazurkiewicz. Trace theory. In Petri Nets: Applications and Relationships to Other Models of Concurrency, pages 279–324. Springer-Verlag (LNCS 255), 1986.

    Google Scholar 

  13. Robin Milner. Communication and Concurrency. Prentice Hall International Series In Computer Science, C. A. R. Hoare series editor, 1989.

    Google Scholar 

  14. Madhavan Mukund and Mogens Nielsen. CCS, Locations and Asynchronous Transition Systems. Proc. Foundations of Software Technology and Theoretical Computer Science 12, pages 328–341, 1992.

    Google Scholar 

  15. Antoni Mazurkiewicz, Edward Ochmański, and Wojciech Penczek. Concurrent systems and inevitability. Theoretical Computer Science, 64:281–304, 1989.

    Google Scholar 

  16. Zohar Manna and Amir Puneli. The Temporal Logic of Reactive and Concurrent Systems. Springer Verlag, 1992.

    Google Scholar 

  17. Ernst R. Olderog. Nets, Terms and Formulas. Cambridge University Press, 1991. Number 23 Tracts in Theoretical Computer Science.

    Google Scholar 

  18. Wojciech Penzcek. Temporal logics for trace systems: On automated verification. International Journal of Foundations of Computer Science, 4 (1):31–67, 1993.

    Google Scholar 

  19. Doron Peled and Amir Pnueli. Proving partial order liveness properties. In Proc. ICALP'90, pages 553–571. Springer-Verlag (LNCS 443), 1990.

    Google Scholar 

  20. Wolfgang Reisig. Petri Nets — An Introduction. EATCS Monographs in Computer Science Vol.4, 1985.

    Google Scholar 

  21. M. W. Shields. Concurrent machines. Computer Journal, 28:449–465, 1985.

    Google Scholar 

  22. Eugene W. Stark. Concurrent transition systems. Theoretical Computer Science, 64:221–269, 1989.

    Google Scholar 

  23. Colin P. Stirling and David Walker. Local model checking in the modal mu-calculus. Technical Report ECS-LFCS-89-78, Laboratory for Foundations of Computer Science, Department of Computer Science-University of Edinburgh, May 1989.

    Google Scholar 

  24. Glynn Winskel. Event structures. In Petri Nets: Applications and Relationships to Other Models of Concurrency, pages 325–390. Springer-Verlag (LNCS 255), 1986.

    Google Scholar 

  25. Glynn Winskel and Mogens Nielsen. Models for concurrency. Research Series RS-94-12, BRICS, Department of Computer Science, University of Aarhus, May 1994. 144 pp. To appear as a chapter in the Handbook of Logic and the Foundations of Computer Science, Oxford University Press.

    Google Scholar 

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V. S. Alagar Maurice Nivat

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© 1995 Springer-Verlag Berlin Heidelberg

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Cheng, A. (1995). Petri nets, traces, and local model checking. In: Alagar, V.S., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1995. Lecture Notes in Computer Science, vol 936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60043-4_62

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  • DOI: https://doi.org/10.1007/3-540-60043-4_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60043-5

  • Online ISBN: 978-3-540-49410-2

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