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Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling

  • Håkan L. S. Younes
  • Reid G. Simmons
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2404)

Abstract

We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in two senses. First, the properties, expressed as CSL formulas, can be probabilistic. Second, the result of the verification is probabilistic, and the probability of error is bounded by two parameters passed to the verification procedure. The verification of properties can be carried out in an anytime manner by starting off with loose error bounds, and gradually tightening these bounds.

Keywords

Error Bound Sample Path Probabilistic Operator Discrete Event System Execution Path 
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.

References

  1. [1]
    Rajeev Alur, Costas Courcoubetis, and David Dill. Model-checking for real-time systems. In Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science, pages 414–425, Philadelphia, PA, June 1990. IEEE Computer Society Press.Google Scholar
  2. [2]
    Rajeev Alur, Costas Courcoubetis, and David Dill. Model-checking for probabilistic real-time systems. In Leach Albert, B. Monien, and M. Rodríguez Artalejo editors, Proceedings of the 18th International Colloquium on Automata, Languages and Programming, volume 510 of Lecture Notes in Computer Science, pages 115–126, Madrid, Spain, July 1991. Springer.Google Scholar
  3. [3]
    Adnan Aziz, Kumud Sanwal, Vigyan Singhal, and Robert Brayton. Verifying continuous time Markov chains. In Rajeev Alur and Thomas A. Henzinger, editors, Proceedings of the 8th International Conference on Computer Aided Verification, volume 1102 of Lecture Notes in Computer Science, pages 269–276, New Brunswick, NJ, July/August 1996. Springer.Google Scholar
  4. [4]
    Adnan Aziz, Kumud Sanwal, Vigyan Singhal, and Robert Brayton. Model-checking continuous-time Markov chains. ACM Transactions on Computational Logic, 1(1):162–170, July 2000.Google Scholar
  5. [5]
    Christel Baier, Joost-Pieter Katoen, and Holger Hermanns. Approximate symbolic model checking of continuous-time Markov chains. In Jos C. M. Baeten and Sjouke Mauw, editors, Proceedings of the 10th International Conference on Concurrency Theory, volume 1664 of Lecture Notes in Computer Science, pages 146–161, Eindhoven, the Netherlands, August 1999. Springer.Google Scholar
  6. [6]
    James R. Bitner and Edward M. Reingold. Backtrack programming techniques. Communications of the ACM, 18(11):651–656, November 1975.Google Scholar
  7. [7]
    E. M. Clarke, E. Allen Emerson, and A. Prasad Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2):244–263, April 1986.Google Scholar
  8. [8]
    Peter W. Glynn. A GSMP formalism for discrete event systems. Proceedings of the IEEE, 77(1):14–23, January 1989.Google Scholar
  9. [9]
    Peter W. Glynn and Donald L. Iglehart. Simulation methods for queues: An overview. Queueing Systems, 3:221–255, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Hans Hansson and Bengt Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6(5):512–535, 1994.zbMATHCrossRefGoogle Scholar
  11. [11]
    Ronald A. Howard. Dynamic Probabilistic Systems, volume II. John Wiley & Sons, New York, NY, 1971.Google Scholar
  12. [12]
    Gabriel G. Infante López, Holger Hermanns, and Joost-Pieter Katoen. Beyond memoryless distributions: Model checking semi-Markov chains. In Luca de Alfaro and Stephen Gilmore, editors, Proceedings of the 1st Joint International PAPM-PROBMIV Workshop, volume 2165 of Lecture Notes in Computer Science, pages 57–70, Aachen, Germany, September 2001. Springer.Google Scholar
  13. [13]
    Marta Kwiatkowska, Gethin Norman, Roberto Segala, and Jeremy Sproston. Verifying quantitative properties of continuous probabilistic timed automata. In Catuscia Palamidessi, editor, Proceedings of the 11th International Conference on Concurrency Theory, volume 1877 of Lecture Notes in Computer Science, pages 123–137, State College, PA, August 2000. Springer.Google Scholar
  14. [14]
    Klaus Matthes. Zur Theorie der Bedienungsprozesse. In Jaroslav Kožešník, editor, Transactions of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, pages 513–528, Liblice, Czechoslovakia, June 1962. Publishing House of the Czechoslovak Academy of Sciences.Google Scholar
  15. [15]
    Gerald S. Shedler. Regenerative Stochastic Simulation. Academic Press, Boston, MA, 1993.zbMATHGoogle Scholar
  16. [16]
    Abraham Wald. Sequential tests of statistical hypotheses. Annals of Mathematical Statistics, 16(2):117–186, June 1945.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Håkan L. S. Younes
    • 1
  • Reid G. Simmons
    • 1
  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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