Skip to main content
SpringerLink
Log in

An Axiomatization of Probabilistic Testing

  • Conference paper
  • First Online:
Book cover Formal Methods for Real-Time and Probabilistic Systems (ARTS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1601))

Abstract

In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19].

Research partially supported by the CICYT projects TIC 94-0851-C02-02 and TIC 97-0669-C03-01.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.C.M. Baeten, J.A. Bergstra, and S.A. Smolka. Axiomatizing probabilistic processes: ACP with generative probabilities. Information and Computation, 121(2):234–255, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Baier and H. Hermanns. Weak bisimulation for fully probabilistic processes. In Computer Aided Verification’97, LNCS 1254, pages 119–130. Springer, 1997.

    Chapter  Google Scholar 

  3. I. Christoff. Testing equivalences and fully abstract models for probabilistic processes. In CONCUR’90, LNCS 458, pages 126–140. Springer, 1990.

    Google Scholar 

  4. 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 

  5. R. Cleaveland, S.A. Smolka, and A.E. Zwarico. Testing preorders for probabilistic processes. In 19th ICALP, LNCS 623, pages 708–719. Springer, 1992.

    Google Scholar 

  6. F. Cuartero, D. de Frutos, and V. Valero. A sound and complete proof system for probabilistic processes. In 4th International AMAST Workshop on Real-Time Systems, Concurrent and Distributed Software, LNCS 1231, pages 340–352. Springer, 1997.

    Google Scholar 

  7. P.R. D’Argenio, H. Hermanns, and J.-P. Katoen. On generative parallel composition. In Workshop on Probabilistic Methods in Verification, PROBMIV’98, pages 105–121, 1998.

    Google Scholar 

  8. R. de Nicola and M.C.B. Hennessy. Testing equivalences for processes. Theoretical Computer Science, 34:83–133, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Giacalone, C.-C. Jou, and S.A. Smolka. Algebraic reasoning for probabilistic concurrent systems. In Proceedings of Working Conference on Programming Concepts and Methods, IFIP TC 2. North Holland, 1990.

    Google Scholar 

  10. 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 

  11. C. Gregorio and M. Núñez. Denotational semantics for probabilistic refusal testing. In Workshop on Probabilistic Methods in Verification, PROBMIV’98, pages 123–137, 1998.

    Google Scholar 

  12. M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.

    Google Scholar 

  13. C.-C. Jou and S.A. Smolka. Equivalences, congruences and complete axiomatizations for probabilistic processes. In CONCUR’90, LNCS 458, pages 367–383. Springer, 1990.

    Google Scholar 

  14. K. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94(1):1–28, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  15. K.G. Larsen and A. Skou. Compositional verification of probabilistic processes. In CONCUR’92, LNCS 630, pages 456–471. Springer, 1992.

    Google Scholar 

  16. G. Lowe. Probabilistic and prioritized models of timed CSP. Theoretical Computer Science, 138:315–352, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Núñez. Semánticas de Pruebas para Álgebras de Procesos Probabilśticos. PhD thesis, Universidad Complutense de Madrid, 1996.

    Google Scholar 

  18. M. Núñez and D. de Frutos. Testing semantics for probabilistic LOTOS. In Formal Description Techniques VIII, pages 365–380. Chapman & Hall, 1995.

    Google Scholar 

  19. 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 

  20. E.W. Stark and S.A. Smolka. A complete axiom system for finite-state probabilistic processes, 1996.

    Google Scholar 

  21. C. Tofts. A synchronous calculus of relative frequency. In CONCUR’90, LNCS 458, pages 467–480. Springer, 1990.

    Google Scholar 

  22. 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.

    Article  MathSciNet  MATH  Google Scholar 

  23. 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 

  24. S. Yuen, R. Cleaveland, Z. Dayar, and S.A. Smolka. Fully abstract characterizations of testing preorders for probabilistic processes. In CONCUR’94, LNCS 836, pages 497–512. Springer, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. de Sistemas Informáticos y Programación, Universidad Complutense de Madrid, Spain

    Manuel Núñez

Authors
  1. Manuel Núñez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Lehrstuhl für Informatik, University of Erlangen-Nürnberg, Martensstr. 3, D-91058, Erlangen, Germany

    Joost-Pieter Katoen

  2. Formal Methods and Tools Group, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Joost-Pieter Katoen

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Núñez, M. (1999). An Axiomatization of Probabilistic Testing. In: Katoen, JP. (eds) Formal Methods for Real-Time and Probabilistic Systems. ARTS 1999. Lecture Notes in Computer Science, vol 1601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48778-6_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-48778-6_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66010-1

  • Online ISBN: 978-3-540-48778-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation