Skip to main content
SpringerLink
Log in

Deciding bisimulation-like equivalences with finite-state processes

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

Included in the following conference series:

Abstract

We design a general method for proving decidability of bisimulation-like equivalences between infinite-state processes and finite-state ones. We apply this method to the class of PAD processes, which strictly subsumes PA and push-down (PDA) processes, showing that a large class of bisimulation-like equivalences (including e.g. strong and weak bisimilarity) is decidable between PAD and finite-state processes. On the other hand, we also demonstrate that no ‘reasonable’ bisimulation-like equivalence is decidable between state-extended PA processes and finite-state ones. Furthermore, weak bisimilarity with finite-state processes is shown to be undecidable even for state-extended BPP (which are also known as ‘parallel pushdown processes’).

The first author is supported by the Grant Agency of the Czech Republic, grant No. 201/97/0456. The second author is supported by a Post-Doc grant GA čR No. 201/98/P046 and by a Research Fellowship granted by The Alexander von Humboldt Foundation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Proceedings of CONCUR'96, volume 1119 of LNCS. Springer-Verlag, 1996.

    Google Scholar 

  2. Proceedings of CONCUR'97, volume 1243 of LNCS. Springer-Verlag, 1997.

    Google Scholar 

  3. J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. Decidability of bisimulation equivalence for processes generating context-free languages. JACM, 40:653–682, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  4. I. černá, M. KŘetínský, and A. Kučera. Bisimilarity is decidable in the union of normed BPA and normed BPP processes. ENTCS, 6, 1997.

    Google Scholar 

  5. S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation is decidable for all basic parallel processes. In Proceedings of CONCUR'93, volume 715 of LNCS, pages 143–157. Springer-Verlag, 1993.

    Google Scholar 

  6. S. Christensen, H. Hüttel, and C. Stirling. Bisimulation equivalence is decidable for all context-free processes. Information and Computation, 121:143–148, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Esparza. Petri nets, commutative context-free grammars, and basic parallel processes. In Proceedings of FCT'95, volume 965 of LNCS, pages 221–232. Springer-Verlag, 1995.

    Google Scholar 

  8. P. Jančar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281–301, 1995.

    Article  MathSciNet  Google Scholar 

  9. P. Jančar and J. Esparza. Deciding finiteness of Petri nets up to bisimilarity. In Proceedings of ICALP'96, volume 1099 of LNCS, pages 478–489. Springer-Verlag, 1996.

    Google Scholar 

  10. P. Jančar and A. Kučera. Bisimilarity of processes with finite-state systems. ENTCS, 9, 1997.

    Google Scholar 

  11. P. Jančar, A. Kučera, and R. Mayr. Deciding bisimulation-like equivalences with finite-state processes. Technical report TUM-I9805, Technische Universität München, 1998.

    Google Scholar 

  12. P. Jančar and F. Moller. Checking regular properties of Petri nets. In Proceedings of CONCUR'95, volume 962 of LNCS, pages 348–362. Springer-Verlag, 1995.

    Google Scholar 

  13. A. Kučera. How to parallelize sequential processes. In Proceedings of CONCUR'97 [2], pages 302–316.

    Google Scholar 

  14. R. Mayr. Weak bisimulation and model checking for basic parallel processes. In Proceedings of FST&TCS'96, volume 1180 of LNCS, pages 88–99. Springer-Verlag, 1996.

    Google Scholar 

  15. R. Mayr. Model checking PA-processes. In Proceedings of CONCUR'97 [2], pages 332–346.

    Google Scholar 

  16. R. Mayr. Process rewrite systems. ENTCS, 7, 1997.

    Google Scholar 

  17. R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-München, 1998.

    Google Scholar 

  18. R. Milner. Communication and Concurrency. Prentice-Hall, 1989.

    Google Scholar 

  19. F. Moller. Infinite results. In Proceedings of CONCUR'96 [1], pages 195–216.

    Google Scholar 

  20. D.M.R. Park. Concurrency and automata on infinite sequences. In Proceedings 5th GI Conference, volume 104 of LNCS, pages 167–183. Springer-Verlag, 1981.

    Google Scholar 

  21. B. Steffen and A. Ingólfsdóttir. Characteristic formulae for processes with divergence. Information and Computation, 110(1):149–163, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  22. C. Stirling. Decidability of bisimulation equivalence for normed pushdown processes. In Proceedings of CONCUR'96 [1], pages 217–232.

    Google Scholar 

  23. R.J. van Glabbeek and W.P. Weijland. Branching time and abstraction in bisimulation semantics. Information Processing Letters, 89:613–618, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science FEI, Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic

    Petr Jančar

  2. Faculty of Informatics MU, Botanická 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

  3. Institut für Informatik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany

    Richard Mayr

Authors
  1. Petr Jančar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonín Kučera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard Mayr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kim G. Larsen Sven Skyum Glynn Winskel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jančar, P., Kučera, A., Mayr, R. (1998). Deciding bisimulation-like equivalences with finite-state processes. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055053

Download citation

  • DOI: https://doi.org/10.1007/BFb0055053

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation