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Decidability of Strong Bisimilarity for Timed BPP

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CONCUR 2002 — Concurrency Theory (CONCUR 2002)

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Abstract

We investigate a timed extension of the class of Basic Parallel Processes (BPP), in which actions are durational and urgent and parallel components have independent local clocks. The main result is decidability of strong bisimilarity, known also as performance equivalence, in this class. This extends the earlier decidability result for plain BPP [8] as well as decidability for timed BPP with strictly positive durations of actions [3]. Both ill-timed and well-timed semantics are treated. Our decision procedure is based on decidability of the validity problem for Presburger arithmetic.

This work has been supported by the fellowship of the Foundation for Polish Science, during the author’s post-doc stay at Laboratoire Specification et Verification, ENS Cachan. Partially supported by the KBN grant 7 T11C 002 21 and by the Research Training Network Games.

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References

  1. L. Aceto and D. Murphy. Timing and causality in process algebra. Acta Informatica, 33(4):317–350, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. C. M. Baeten and C. A. Middelburg. Process algebra with timing: real time and discrete time. In J. Bergstra, A. Ponse, S. Smolka, eds., Handbook of Process Algebra, chapter 10, pages 627–684, 2001.

    Google Scholar 

  3. B. Bérard, A. Labroue, and P. Schnoebelen. Verifying performance equivalence for timed Basic Parallel Processes. In Proc. 3rd Int. Conf. Foundations of Software Science and Computation Structures (FOSSACS’2000), LNCS 1784, pages 35–47, 2000.

    Google Scholar 

  4. O. Burkart, D. Caucal, F Moller, and B. Steffen. Verification of infinite structures. In J. Bergstra, A. Ponse, S. Smolka, eds., Handbook of Process Algebra, chapter 9, pages 545–623, 2001.

    Google Scholar 

  5. D. Caucal. Graphes canoniques des graphes algebraiques. Informatique Theoretique et Applications (RAIRO), 24(4):339–352, 1990.

    MATH  MathSciNet  Google Scholar 

  6. K. Čerāns. Decidability of bisimulation equivalence for parallel timer processes. In Proc. CAV’92, LNCS 663, 1992.

    Google Scholar 

  7. S. Christensen. Decidability and Decomposition in process algebras. PhD thesis, Dept. of Computer Science, University of Edinbourg, UK, 1993. PhD Thesis CST-105-93.

    Google Scholar 

  8. S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation equivalence is decidable for Basic Parallel Processes. In Proc. 4th Int. Conf. Concurrency Theory (CONCUR’ 93), LNCS 713, pages 143–157, 1993.

    Google Scholar 

  9. F. Corradini. On performance congruences for process algebras. Information and Computation, 145(2):191–230, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Corradini, R. Gorrieri, and M. Roccetti. Performance preorder and competitive equivalence. Acta Informatica, 34(11):805–835, 1997.

    Article  MathSciNet  Google Scholar 

  11. F. Corradini and M. Pistore. Specification and verification of lazy timed systems. In Proc. 21th Int. Symp. math. Found. Comp. Sci. (MFCS’96), LNCS 1113, pages 279–290, 1996.

    Google Scholar 

  12. S. Eilenberg and M. P. Schuetzenberger. Rational sets in commutative monoids. J. of Algebra, 13:173–191, 1969.

    Article  MATH  Google Scholar 

  13. S. Ginsburg and E. Spanier. Semigroups, Presburger formulas, and languages. Pacific J. of Mathematics, 16(2):285–296, 1966.

    MATH  MathSciNet  Google Scholar 

  14. R. Gorrieri, M. Roccetti, and E. Stancampiano. A theory of processes with durational actions. Theoretical Computer Science, 140(1):73–94, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  15. Y. Hirshfeld. Petri nets and the equivalence problem. In Proc. Computer Science Logic (CSL’93), LNCS 832, pages 165–174, 1993.

    Google Scholar 

  16. Y. Hirshfeld. Congruences in commutative semigroups. LFCS report ECS-LFCS-94-291, Laboratory for Foundations of Computer Science, University of Edinbourg, 1994.

    Google Scholar 

  17. H. Hüttel. Undecidable equivalences for basic parallel processes. In Proc. TACS’94, LNCS 789, pages 454–464, 1994.

    Google Scholar 

  18. P. Jančar. Decidability questions for bisimilarity of Petri nets and some related problems. In Proc. 11th International Symposium on Theoretical Aspects of Computer Science (STACS’94), Caen, France, LNCS 775, pages 581–592, 1994.

    Google Scholar 

  19. R. Milner. Communication and Concurrency. Prentice Hall, 1989.

    Google Scholar 

  20. F. Moller and C. Tofts. Relating processes with respect to speed. In Proc. 2nd Int Conf. Concurrency Theory (CONCUR’91), LNCS 527, pages 424–438, 1991.

    Google Scholar 

  21. D. C. Oppen. A 22 2 pn upper bound on the complexity of Presburger arithmetic. J. of Comp. and System Sciences, 16:323–332, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  22. J. Srba. Note on the tableau technique for commutative transition systems. In Proc. 5th Foundations of Software Science and Computation Structures (FOSSACS’02), LNCS 2303, pages 387–401, 2002.

    Google Scholar 

  23. J. Srba. Strong bisimilarity and regularity of Basic Parallel Processes is PSPACEhard. In Proc. 19th International Symposium on Theoretical Aspects of Computer Science (STACS’02), LNCS 2285, 2002.

    Google Scholar 

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Lasota, S. (2002). Decidability of Strong Bisimilarity for Timed BPP. In: Brim, L., Křetínský, M., Kučera, A., Jančar, P. (eds) CONCUR 2002 — Concurrency Theory. CONCUR 2002. Lecture Notes in Computer Science, vol 2421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45694-5_37

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  • DOI: https://doi.org/10.1007/3-540-45694-5_37

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