Acta Informatica

, Volume 46, Issue 3, pp 169–191 | Cite as

Hardness of equivalence checking for composed finite-state systems

Original Article

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balcázar J., Gabarró J., Sántha M.: Deciding bisimilarity is P-complete. Formal Aspects Comput. 4(6A), 638–648 (1992)MATHCrossRefGoogle Scholar
  2. 2.
    Chandra A.K., Kozen D.C., Stockmeyer L.J.: Alternation. J. ACM. 28(1), 114–133 (1981)MATHCrossRefMathSciNetGoogle Scholar
  3. 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. 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)Google Scholar
  5. 5.
    Hoare C.A.R.: Communcating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)Google Scholar
  6. 6.
    Immerman, N.: Descriptive Complexity, pp. 53–54. Springer, Heidelberg (1998)Google Scholar
  7. 7.
    Jančar, P., Srba, J.: Undecidability of bisimilarity by Defender’s forcing. J. ACM. 55(1) (2008)Google Scholar
  8. 8.
    Kanellakis P.C., Smolka S.A.: CCS expressions, finite state processes, and three problems of equivalence. Inf. Comput. 86(1), 43–68 (1990)MATHCrossRefMathSciNetGoogle Scholar
  9. 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)Google Scholar
  10. 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)MATHMathSciNetGoogle Scholar
  11. 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)Google Scholar
  12. 12.
    Milner R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  13. 13.
    Paige R., Tarjan R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Rabinovich A.: Complexity of equivalence problems for concurrent systems of finite agents. Inf. Comput. 139(2), 111–129 (1997)MATHCrossRefMathSciNetGoogle Scholar
  15. 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)Google Scholar
  16. 16.
    Sawa Z., Jančar P.: Behavioural equivalences on finite-state systems are PTIME-hard. Comput. Inform. 24(5), 513–528 (2005)MATHMathSciNetGoogle Scholar
  17. 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)Google Scholar
  18. 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)Google Scholar
  19. 19.
    Warmuth M.K., Haussler D.: On the complexity of iterated shuffle. J. Comp. Syst. Sci. 28(3), 345–358 (1984)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.FEITechnical University of OstravaOstrava-PorubaCzech Republic

Personalised recommendations