Advertisement

Optimal simulations, nets and reachability graphs

  • Ryszard Janicki
  • Maciej Koutny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 524)

Abstract

Reasoning about the dynamic properties of a concurrent system can be made easier by avoiding the combinatorial explosion of its state space. One of the ways in which this might be achieved is by using the optimal simulation - a kind of reachability relation on the system's histories. The optimal simulation usually involves only a very small subset of the possible behaviours generated by the system, yet provides a sufficient information to reason about a number of interesting system's properties such as deadlock-freeness and liveness. In this paper we present also other properties of that kind. We then show how the optimal simulation can be used to generate a reachability graph which is usually much smaller than the standard reachability graph of the system. In spite of this both graphs essentially convey the same information about the system's behaviour.

Keywords

Petri nets reachability graphs state-space generation traces partial order semantics step sequences liveness deadlock-freeness verification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8. References

  1. [CF69]
    Cartier P., Foata D., Problemes combinatoires de communication et rearrangements, Lecture Notes in Mathematics 85, Springer 1969.Google Scholar
  2. [CG87]
    Clarke E.M., Grümberg O., Research on Automatic Verification of Finite-State Concurrent Systems, Ann. Rev. Comp. Sci. 2(1987), 269–290.Google Scholar
  3. [CES86]
    Clarke E.M., Emerson E.A., Sistla A.P., Automatic Verification of Finite-State Systems using Temporal Logic Specifications, ACM Transactions on Programming Languages and Systems 8(1986), 244–263.Google Scholar
  4. [God91]
    Godefroid P., Using Partial Orders to Improve Automatic Verification Methods, Proc. of the Computer-Aided Verification Workshop, 1990, to appear in the Lecture Notes in Computer Science.Google Scholar
  5. [HM85]
    Hennessy M. and Milner R., Algebraic Laws for Nondeterminism and Concurrency, JACM 32(1985), 136–161.Google Scholar
  6. [Hoa85]
    Hoare C.A.R., Communicating Sequential Processes, Prentice-Hall, 1985.Google Scholar
  7. [JLKD86]
    Janicki R., Lauer P.E., Koutny M., Devillers R., Concurrent and Maximally Concurrent Evolution of Non-Sequential Systems, Theoretical Computer Science 43(1986), 213–238.Google Scholar
  8. [JK89]
    Janicki R., Koutny M., Towards a Theory of Simulation for Verification of Concurrent Systems, Lecture Notes in Computer Science 366, Springer 1989, 73–88.Google Scholar
  9. [JK89a]
    Janicki R., Koutny M., Optimal Simulation for Verification of Concurrent Systems, Technical Report No. 89-05, McMaster University,Hamilton, Ontario, 1989.Google Scholar
  10. [JK90]
    Janicki R., Koutny M., Net Implementation of Optimal Simulation, in: Proc. of the 11th Conference on Application and Theory of Petri Nets, Paris, June 1990, pp. 295–314.Google Scholar
  11. [JK91]
    Janicki R., Koutny M., Using Optimal Simulations to Reduce Reachability Graphs, Proc. of the Computer-Aided Verification Workshop, 1990, to appear in the Lecture Notes in Computer Science, Springer-Verlag.Google Scholar
  12. [Jen87]
    Jensen K., Coloured Petri Nets, LNCS 254, Springer 1987, pp. 248–299.Google Scholar
  13. [Kel76]
    Keller R.M., Formal Verification of Concurrent Programs, CACM 19(7), 1976, 371–384.Google Scholar
  14. [LSC81]
    Lauer P.E., Shields M.W., Cotronis J.Y., Formal Behavioural Specification of Concurrent Systems without Globality Assumptions, Lecture Notes in Computer Science 107, Springer 1981, 115–151.Google Scholar
  15. [MS82]
    Martinez J., Silva M., A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net, Informatik-Fachberichte 52, Springer 1982, 301–310.Google Scholar
  16. [Maz77]
    Mazurkiewicz A., Concurrent Program Schemes and Their Interpretations, DAIMI-PB-78, Aarhus University, 1977.Google Scholar
  17. [Maz86]
    Mazurkiewicz A., Trace Theory, Lecture Notes in Computer Science 255, Springer 1986, 297–324.Google Scholar
  18. [Mil80]
    Milner R., A Calculus of Communicating Systems, Lecture Notes in Computer Science 92, Springer 1980.Google Scholar
  19. [MR87]
    Morgan E.T, Razouk R.R., Interactive State-Space Analysis of Concurrent Systems, IEEE Transactions on Software Engineering 13(10), 1987.Google Scholar
  20. [Rei85]
    Reisig W., Petri Nets, Springer 1985.Google Scholar
  21. [Tau89]
    Taubner D., Finite Representations of CCS and TCSP Programs by Automata and Petri Nets, Lecture Notes in Computer Science 369, Springer 1989.Google Scholar
  22. [Val89]
    Valmari A., Stubborn Sets for Reduced State Space Generation, Proceedings of the 10th International Conference on Application and Theory of Petri Nets, Bonn, June 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ryszard Janicki
    • 1
  • Maciej Koutny
    • 2
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada
  2. 2.Computing LaboratoryThe University of Newcastle upon TyneNewcastle upon TyneU.K.

Personalised recommendations