Skip to main content
SpringerLink
Log in
Book cover

International Conference on Relational Methods in Computer Science

RelMiCS 2008: Relations and Kleene Algebra in Computer Science pp 304–319Cite as

Reactive Probabilistic Programs and Refinement Algebra

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

Abstract

A trace semantics is given for a probabilistic reactive language which is capable of modelling probabilistic action systems. It is shown that reactive probabilistic programs with the trace semantics form a general refinement algebra. The abstract-algebraic characterisation means that the proofs of earlier-established transformation rules can be reused for probabilistic action systems with trace semantics.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Back, R.J.R., von Wright, J.: Trace refinement of action systems. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 367–384. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  2. Desharnais, J., Möller, B., Struth, G.: Algebraic notions of termination. Technical Report 2006-23, Institute of Computer Science, University of Augsburg (2006)

    Google Scholar 

  3. Hayes, I.J., Utting, M.: A sequential real-time refinement calculus. Acta Informatica 37(6), 385–448 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall, Englewood Cliffs (1998)

    Google Scholar 

  5. Höfner, P., Struth, G.: Algebraic notions of non-termination. Technical Report CS-06-12, Department of Computer Science, University of Sheffield (2006)

    Google Scholar 

  6. McIver, A.K., Cohen, E., Morgan, C.C.: Using probabilistic Kleene algebra for protocol verification. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 296–310. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Meinicke, L.A., Hayes, I.J.: Reasoning algebraically about probabilistic loops. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 380–399. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Meinicke, L.A., Solin, K.: Refinement algebra for probabilistic programs. In: Boiten, E., Derrick, J., Smith, G. (eds.) REFINE (to appear in ENTCS, 2007)

    Google Scholar 

  9. Möller, B.: Lazy Kleene algebra. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 252–273. Springer, Heidelberg (2004)

    Google Scholar 

  10. Morgan, C.C., McIver, A.K.: Cost analysis of games, using program logic. In: APSEC 2001, p. 351. IEEE Computer Society Press, Washington, DC, USA (2001)

    Google Scholar 

  11. Segala, R.: A compositional trace-based semantics for probabilistic automata. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 234–248. Springer, Heidelberg (1995)

    Google Scholar 

  12. Sere, K., Troubitsyna, E.A.: Probabilities in action systems. In: Proc. of the 8th Nordic Workshop on Programming Theory (1996)

    Google Scholar 

  13. Solin, K.: On two dually nondeterministic refinement algebras. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 373–387. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Solin, K., von Wright, J.: Refinement algebra with operators for enabledness and termination. In: Uustalu, T. (ed.) MPC 2006. LNCS, vol. 4014, pp. 397–415. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Takai, T., Furusawa, H.: Monodic tree Kleene algebra. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 402–416. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Troubitsyna, E.A.: Reliability assessment through probabilistic refinement. Nordic Journal of Computing, 320–342 (1999)

    Google Scholar 

  17. von Wright, J.: From Kleene algebra to refinement algebra. In: Boiten, E.A., Möller, B. (eds.) MPC 2002. LNCS, vol. 2386, pp. 233–262. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. von Wright, J.: Towards a refinement algebra. Science of Computer Programming 51, 23–45 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Åbo Akademi, Finland

    L. A. Meinicke & K. Solin

Authors
  1. L. A. Meinicke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Solin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rudolf Berghammer Bernhard Möller Georg Struth

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Meinicke, L.A., Solin, K. (2008). Reactive Probabilistic Programs and Refinement Algebra. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78913-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation