Skip to main content
SpringerLink
Log in

Hardness of equivalence checking for composed finite-state systems

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

Computational complexity of comparing behaviours of systems composed from interacting finite-state components is considered. The main result shows that the respective problems are EXPTIME-hard for all relations between bisimulation equivalence and trace preorder, as conjectured by Rabinovich (Inf Comput 139(2):111–129, 1997). The result is proved for a specific model of parallel compositions where the components synchronize on shared actions but it can be easily extended to other similar models,   to labelled 1-safe Petri nets. Further hardness results are shown for special cases of acyclic systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balcázar J., Gabarró J., Sántha M.: Deciding bisimilarity is P-complete. Formal Aspects Comput. 4(6A), 638–648 (1992)

    Article  MATH  Google Scholar 

  2. Chandra A.K., Kozen D.C., Stockmeyer L.J.: Alternation. J. ACM. 28(1), 114–133 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  3. van Glabbeek R.: Handbook of process algebra. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, chap. The Linear Time—Branching Time Spectrum, pp. 3–99. Elsevier, Amsterdam (2001)

    Google Scholar 

  4. Groote, J.F., Moller, F.: Verification of parallel systems via decomposition. In: Proceedings of Third International Conference on Concurrency Theory. Lecture Notes in Computer Science, vol. 630, pp. 62–76. Springer, Heidelberg (1992)

  5. Hoare C.A.R.: Communcating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)

    Google Scholar 

  6. Immerman, N.: Descriptive Complexity, pp. 53–54. Springer, Heidelberg (1998)

    Google Scholar 

  7. Jančar, P., Srba, J.: Undecidability of bisimilarity by Defender’s forcing. J. ACM. 55(1) (2008)

  8. Kanellakis P.C., Smolka S.A.: CCS expressions, finite state processes, and three problems of equivalence. Inf. Comput. 86(1), 43–68 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  9. Laroussinie, F., Schnoebelen, P.: The state explosion problem from trace to bisimulation equivalence. In: Proceedings of the 3rd International Conference Foundations of Software Science and Computation Structures (FOSSACS’2000), Berlin, Germany, March–April 2000. Lecture Notes in Computer Science, vol. 1784, pp. 192–207. Springer, Heidelberg (2000)

  10. Mansfield, A.: On the computational complexity of a merge recognition problem. DAMATH: Discrete Appl. Math. Combin. Oper. Res. Comput. Sci. 5, 119–122 (1983)

    MATH  MathSciNet  Google Scholar 

  11. Meyer, A.R., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential space. In: 13th Annual Symposium on Switching and Automata Theory, pp. 125–129. IEEE, New York (1972)

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

    MATH  Google Scholar 

  13. Paige R., Tarjan R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  14. Rabinovich A.: Complexity of equivalence problems for concurrent systems of finite agents. Inf. Comput. 139(2), 111–129 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sawa, Z.: Equivalence checking of non-flat systems is EXPTIME-hard. In: Proceedings of CONCUR 2003. Lecture Notes in Computer Science, vol. 2761, pp. 237–250. Springer, Heidelberg (2003)

  16. Sawa Z., Jančar P.: Behavioural equivalences on finite-state systems are PTIME-hard. Comput. Inform. 24(5), 513–528 (2005)

    MATH  MathSciNet  Google Scholar 

  17. Shukla, S.K., Hunt, H.B., Rosenkrantz, D.J., Stearns, R.E.: On the complexity of relational problems for finite state processes. In: Proceedings of ICALP’96. Lecture Notes in Computer Science, vol. 1099, pp. 466–477. Springer, Heidelberg (1996)

  18. Valmari, A., Kervinen, A.: Alphabet-based synchronisation is exponentially cheaper. In: Proceedings of CONCUR 2002. Lecture Notes in Computer Science, vol. 2421, pp. 161–176 (2002)

  19. Warmuth M.K., Haussler D.: On the complexity of iterated shuffle. J. Comp. Syst. Sci. 28(3), 345–358 (1984)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FEI, Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava-Poruba, Czech Republic

    Zdeněk Sawa & Petr Jančar

Authors
  1. Zdeněk Sawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petr Jančar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zdeněk Sawa.

Additional information

The authors gratefully acknowledge the support by the Czech Ministry of Education, Grant No. 1M0567.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sawa, Z., Jančar, P. Hardness of equivalence checking for composed finite-state systems. Acta Informatica 46, 169–191 (2009). https://doi.org/10.1007/s00236-008-0088-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-008-0088-x

Keywords

Search

Navigation