Advertisement

A Testing Theory for Generally Distributed Stochastic Processes

Extended Abstract
  • Natalia López
  • Manuel Núñez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2154)

Abstract

In this paper we present a testing theory for stochastic processes. This theory is developed to deal with processes which probability distributions are not restricted to be exponential. In order to define this testing semantics, we compute the probability with which a process passes a test before an amount of time has elapsed. Two processes will be equivalent if they return the same probabilities for any test T and any time t. The key idea consists in joining all the random variables associated with the computations that the composition of process and test may perform. The combination of the values that this random variable takes and the probabilities of executing the actions belonging to the computation will give us the desired probabilities. Finally, we relate our stochastic testing semantics with other notions of testing.

Keywords

Parallel Operator Operational Semantic Testing Theory Visible Action Process Algebra 
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. [ABC+94]
    M. Ajmone Marsan, A. Bianco, L. Ciminiera, R. Sisto, and A. Valenzano. A LOTOS extension for the performance analysis of distributed systems. IEEE/ACM Transactions on Networking, 2(2):151–165, 1994.CrossRefGoogle Scholar
  2. [BB93]
    J.C.M. Baeten and J.A. Bergstra. Real time process algebra. Formal Aspects of Computing, 3:142–188, 1993.CrossRefGoogle Scholar
  3. [BBG98]
    M. Bravetti, M. Bernardo, and R. Gorrieri. Towards performance evaluation with general distributions in process algebras. In CONCUR’98, LNCS 1466, pages 405–422. Springer, 1998.Google Scholar
  4. [BC00]
    M. Bernardo and W.R. Cleaveland. A theory of testing for markovian processes. In CONCUR’2000, LNCS 1877, pages 305–319. Springer, 2000.Google Scholar
  5. [BG98]
    M. Bernardo and R. Gorrieri. A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoretical Computer Science, 202:1–54, 1998.MATHCrossRefMathSciNetGoogle Scholar
  6. [BG01]
    M. Bravetti and R. Gorrieri. The theory of interactive generalized semi-markov processes. To appear in Theoretical Computer Science, 2001.Google Scholar
  7. [BKLL95]
    E. Brinksma, J.-P. Katoen, R. Langerak, and D. Latella. A stochastic causality-based process algebra. The Computer Journal, 38(7):553–565, 1995.CrossRefGoogle Scholar
  8. [BW90]
    J.C.M. Baeten and W.P. Weijland. Process Algebra. Cambridge Tracts in Computer Science 18. Cambridge University Press, 1990.Google Scholar
  9. [CDSY99]
    R. Cleaveland, Z. Dayar, S.A. Smolka, and S. Yuen. Testing preorders for probabilistic processes. Information and Computation, 154(2):93–148, 1999.MATHCrossRefMathSciNetGoogle Scholar
  10. [Chr90]
    I. Christoff. Testing equivalences and fully abstract models for probabilistic processes. In CONCUR’90, LNCS 458, pages 126–140. Springer, 19Google Scholar
  11. [CLLS96]
    R. Cleaveland, I. Lee, P. Lewis, and S.A. Smolka. A theory of testing for soft real-time processes. In 8th International Conference on Software Engineering and Knowledge Engineering, 1996.Google Scholar
  12. [DKB98]
    P.R. D’Argenio, J.-P. Katoen, and E. Brinksma. An algebraic approach to the specification of stochastic systems. In Programming Concepts and Methods, pages 126–147. Chapman & Hall, 1998.Google Scholar
  13. [dNH84]
    R. de Nicola and M.C.B. Hennessy. Testing equivalences for processes. Theoretical Computer Science, 34:83–133, 1984.MATHCrossRefMathSciNetGoogle Scholar
  14. [EKN99]
    A. El-Rayes, M. Kwiatkowska, and G. Norman. Solving infinite stochastic process algebra models through matrix-geometric methods. In 7th International Workshop on Process Algebra and Performance Modelling, pages 41–62, 1999.Google Scholar
  15. [GHR93]
    N. Götz, U. Herzog, and M. Rettelbach. Multiprocessor and distributed system design: The integration of functional specification and performance analysis using stochastic process algebras. In 16th Int. Symp. on Computer Performance Modelling, Measurement and Evaluation (PERFOR-MANCE’93), LNCS 729, pages 121–146. Springer, 1993.Google Scholar
  16. [GLNP97]
    C. Gregorio, L. Llana, M. Núñez, and P. Palao. Testing semantics for a probabilistic-timed process algebra. In 4th International AMAST Workshop on Real-Time Systems, Concurrent, and Distributed Software, LNCS 1231, pages 353–367. Springer, 1997.Google Scholar
  17. [GN99]
    C. Gregorio and M. Núñez. Denotational semantics for probabilistic refusal testing. In PROBMIV’98, Electronic Notes in Theoretical Computer Science 22. Elsevier, 1999.Google Scholar
  18. [GSS95]
    R. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59–80, 1995.MATHCrossRefMathSciNetGoogle Scholar
  19. [Han91]
    H. Hansson. Time and Probability in Formal Design of Distributed Systems. PhD thesis, Department of Computer Systems. Uppsala University, 1991.Google Scholar
  20. [Hen88]
    M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.Google Scholar
  21. [HHK01]
    H. Hermanns, U. Herzog, and J.-P. Katoen. Process algebra for performance evaluation. To appear in Theoretical Computer Science, 2001.Google Scholar
  22. [Hil96]
    J. Hillston. A Compositional Approach to Performance Modelling. Cambridge University Press, 1996.Google Scholar
  23. [Hoa85]
    C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall, 1985.Google Scholar
  24. [HR95]
    M. Hennessy and T. Regan. A process algebra for timed systems. Information and Computation, 117(2):221–239, 1995.MATHCrossRefMathSciNetGoogle Scholar
  25. [HS00]
    P.G. Harrison and B. Strulo. SPADES-a process algebra for discrete event simulation. Journal of Logic Computation, 10(1):3–42, 2000.MATHCrossRefMathSciNetGoogle Scholar
  26. [KN98]
    M. Kwiatkowska and G.J. Norman. A testing equivalence for reactive probabilistic processes. In EXPRESS’98, Electronic Notes in Theoretical Computer Science 16. Elsevier, 1998.Google Scholar
  27. [LdF97]
    L. Llana and D. de Frutos. Denotational semantics for timed testing. In 4th AM AST Workshop on Real-Time Systems, Concurrent and Distributed Software, LNCS 1231, pages 368–382, 1997.Google Scholar
  28. [LN01]
    N. López and M. Núñez. A testing theory for generally distributed stochastic processes. Available at: http://dalila.sip.ucm.es/natalia/papers/stoctesting.ps.gz, 2001.
  29. [Low95]
    G. Lowe. Probabilistic and prioritized models of timed CSP. Theoretical Computer Science, 138:315–352, 1995.MATHCrossRefMathSciNetGoogle Scholar
  30. [LS91]
    K. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94(1):1–28, 1991.MATHCrossRefMathSciNetGoogle Scholar
  31. [Mil81]
    R. Milner. A modal characterization of observable machine-behaviour. In 6th CAAP, LNCS 112, pages 25–34. Springer, 1981.Google Scholar
  32. [Mil89]
    R. Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  33. [NdF95]
    M. Núñez and D. de Frutos. Testing semantics for probabilistic LOTOS. In Formal Description Techniques VIII, pages 365–380. Chapman & Hall, 1995.Google Scholar
  34. [NdFL95]
    M. Núñez, D. de Frutos, and L. Llana. Acceptance trees for probabilistic processes. In CONCUR’95, LNCS 962, pages 249–263. Springer, 1995.Google Scholar
  35. [Neu92]
    M. Neuts. Two further closure properties of Ph-distributions. Asia-Pacific Journal of Operational Research, 9(1):77–85, 1992.MATHMathSciNetGoogle Scholar
  36. [NR99]
    M. Núñez and D. Rupérez. Fair testing through probabilistic testing. In Formal Description Techniques for Distributed Systems and Communication Protocols (XII), and Protocol Specification, Testing, and Verification (XIX), pages 135–150. Kluwer Academic Publishers, 1999.Google Scholar
  37. [NS94]
    X. Nicollin and J. Sifakis. The algebra of timed process, ATP: Theory and application. Information and Computation, 114(1):131–178, 1994.MATHCrossRefMathSciNetGoogle Scholar
  38. [Núñ96]
    M. Núñez. Semánticas de Pruebas paraÁlgebras de Procesos Probabilísticos. PhD thesis, Universidad Complutense de Madrid, 1996.Google Scholar
  39. [RR88]
    G.M. Reed and A.W. Roscoe. A timed model for communicating sequential processes. Theoretical Computer Science, 58:249–261, 1988.MATHCrossRefMathSciNetGoogle Scholar
  40. [YL92]
    W. Yi and K.G. Larsen. Testing probabilistic and nondeterministic processes. In Protocol Specification, Testing and Verification XII, pages 47–61. North Holland, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Natalia López
    • 1
  • Manuel Núñez
    • 1
  1. 1.Dpt. Sistemas Informáticos y ProgramaciónUniversidad Complutense de MadridSpain

Personalised recommendations