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On Decidability of LTL Model Checking for Process Rewrite Systems

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FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4337))

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Abstract

We establish a decidability boundary of the model checking problem for infinite-state systems defined by Process Rewrite Systems (PRS) or weakly extended Process Rewrite Systems (wPRS), and properties described by basic fragments of action-based Linear Temporal Logic (LTL). It is known that the problem for general LTL properties is decidable for Petri nets and for pushdown processes, while it is undecidable for PA processes. As our main result, we show that the problem is decidable for wPRS if we consider properties defined by formulae with only modalities strict eventually and strict always. Moreover, we show that the problem remains undecidable for PA processes even with respect to the LTL fragment with the only modality until or the fragment with modalities next and infinitely often.

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References

  1. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Google Scholar 

  2. Bouajjani, A., Habermehl, P.: Constrained properties, semilinear systems, and petri nets. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 481–497. Springer, Heidelberg (1996)

    Google Scholar 

  3. Bozzelli, L., Křetínský, M., Řehák, V., Strejček, J.: On Decidability of LTL Model Checking for Weakly Extended Process Rewrite Systems. Technical Report FIMU-RS-2006-05, Faculty of Informatics, Masaryk University, Brno (2006); A full version of the paper presented at FSTTCS 2006

    Google Scholar 

  4. Bozzelli, L.: Model checking for process rewrite systems and a class of action-based regular properties. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 282–297. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Esparza, J.: On the decidability of model checking for several mu-calculi and petri nets. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 115–129. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  6. Habermehl, P.: On the complexity of the linear-time μ-calculus for Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 102–116. Springer, Heidelberg (1997)

    Google Scholar 

  7. Křetínský, M., Řehák, V., Strejček, J.: Extended process rewrite systems: Expressiveness and reachability. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 355–370. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Křetínský, M., Řehák, V., Strejček, J.: On extensions of process rewrite systems: Rewrite systems with weak finite-state unit. In: Proceedings of INFINITY 2003. ENTCS, vol. 98, pp. 75–88. Elsevier, Amsterdam (2004)

    Google Scholar 

  9. Křetínský, M., Řehák, V., Strejček, J.: Reachability of hennessy-milner properties for weakly extended PRS. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 213–224. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Lipton, R.: The reachability problem is exponential-space hard. Technical Report 62, Department of Computer Science, Yale University (1976)

    Google Scholar 

  11. Maidl, M.: The common fragment of CTL and LTL. In: Proc. 41st Annual Symposium on Foundations of Computer Science, pp. 643–652 (2000)

    Google Scholar 

  12. Mayr, E.W.: An algorithm for the general Petri net reachability problem. SIAM Journal on Computing 13(3), 441–460 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  13. Mayr, R.: Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, Technische Universität München (1998)

    Google Scholar 

  14. Mayr, R.: Process rewrite systems. Information and Computation 156(1), 264–286 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  16. Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  17. Pnueli, A.: The temporal logic of programs. In: Proc. 18th IEEE Symposium on the Foundations of Computer Science, pp. 46–57 (1977)

    Google Scholar 

  18. Strejček, J.: Linear Temporal Logic: Expressiveness and Model Checking. PhD thesis, Faculty of Informatics, Masaryk University in Brno (2004)

    Google Scholar 

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Bozzelli, L., Křetínský, M., Řehák, V., Strejček, J. (2006). On Decidability of LTL Model Checking for Process Rewrite Systems. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_24

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  • DOI: https://doi.org/10.1007/11944836_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49994-7

  • Online ISBN: 978-3-540-49995-4

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