Advertisement

Checking equivalences between concurrent systems of finite agents (Extended abstract)

  • Alexander Rabinovich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 623)

Abstract

Consider two synchronously communicating systems p and q over finite agents. Assume that one wants to check whether p ∼ q for one of the commonly used equivalences. We show that this question is PSPACE hard for all equivalences which lie between strong bisimulation and trace equivalences. For some equivalences exponential lower and upper bounds are proven. We also show that this problem is NP hard and co-NP hard even for a class of very simple finite agents.

Dataflow nets are the simplest systems of asynchronously communicating agents. Let ∼ be an equivalence which lies between strong bisimulation and trace equivalences. We show that there is no algorithm for checking ∼-equivalence between dataflow nets over finite state agents.

Keywords

Check Equivalence Parallel Composition Label Transition System Finite State Automaton Trace Equivalence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ABGS]
    C. Alvarez, J. Balcazar, J. Gabarro and M. Santa. Parallel Complexity in the design and analysis of concurrent systems. In PARL 91, volume 505 of Lect. Notes in Computer Science. Springer Verlag, 1991.Google Scholar
  2. [Bl]
    B. Bloom. Ready Simulation, Bisimulation, and the Semantics of CCS-like languages. Ph.D. Thesis, Technical Report MIT/LCS/TR-491, 1990.Google Scholar
  3. [BHR]
    S. Brookes, C. Hoare, and A. Roscoe. A theory of communicating sequential processes. J. ACM, 31(3):560–599, 1984.CrossRefGoogle Scholar
  4. [Fu]
    M. Furer. The complexity of inequivalence problem for regular expressions with intersection. In Proc. 7th ICALP, volume 85 of Lect. Notes in Computer Science. Springer Verlag, 1980.Google Scholar
  5. [GM]
    J. F. Groote and F. Moller. Verification of Parallel System via Decomposition. Preliminary Report, CWI 1991.Google Scholar
  6. [GV]
    J. F. Groote and F. Vaandrager. An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. In International Conference on Automata, Languages and Programming, volume 443 of Lect. Notes in Computer Science. Springer Verlag, 90.Google Scholar
  7. [He]
    M. Hennessy. Algebraic Theory of Processes. MIT Press, Cambridge, Massachusetts, 1988.Google Scholar
  8. [Ho]
    C. Hoare. Communicating Sequential Processes. Prentice-Hall International, Englewood Cliffs, 1985.Google Scholar
  9. [HU]
    J. Hopcroft and J. Ullman. Introduction to Automata Theory, Lamguages and Computations, Addison-Wesley, Reading, MA, 1979.Google Scholar
  10. [Hu]
    H. Hunt. The equivalence problem for regular expressions with intersection is not polynomial in tape, Tech. Rep. TR 73-161, Cornell University, 1973.Google Scholar
  11. [MS]
    A. J. Mayer and L. J. Stockmeyer. World Problems — This Time with Interleaving. Technical Report, IBM RJ8180, July, 1991.Google Scholar
  12. [Mi]
    R. Milner. Communication and Concurrency. Prentice-Hall International, Englewood Cliffs, 1989.Google Scholar
  13. [KS]
    P. C. Kanellakis and S. A. Smolka. CCS Expressions, Finite State Processes, and Three Problems of Equivalence. In Information and Computation, volume 86, 1990.Google Scholar
  14. [PT]
    R. Paige and R. Tarjan. Three partition refinement algorithms. SIAM J. Comput., 16(6):973–989, 1987.CrossRefGoogle Scholar
  15. [Pa]
    D. Park. Concurrency and Automata on infinite sequences. volume 104 of Lect. Notes in Computer Science. Springer Verlag, 1981.Google Scholar
  16. [Plo]
    G. Plotkin. A structured approach to operational semantics. FN 19 DAIMI, Aarhus Univ., 1981.Google Scholar
  17. [SM]
    L. J. Stockmeyer and A. R. Meyer. Word Problems Requiring Exponential Time. In Proc. 5th ACM Symp. on Theory of Computing, 1973.Google Scholar
  18. [Sto]
    L. J. Stockmeyer. Private communication, Jan 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Alexander Rabinovich
    • 1
  1. 1.IBM Research DivisionT.J. Watson Research CenterYorktown Heights

Personalised recommendations