Skip to main content

Timed Process Algebra (With a Focus on Explicit Termination and Relative-Timing)

  • Chapter

Part of the Lecture Notes in Computer Science book series (LNCS,volume 3185)

Abstract

We treat theory and application of timed process algebra. We focus on a variant that uses explicit termination and action prefixing. This variant has some advantages over other variants. We concentrate on relative timing, but the treatment of absolute timing is similar. We treat both discrete and dense timing. We build up the theory incrementally. The different algebras are interrelated by embeddings and conservative extensions. As an example, we consider the PAR communication protocol.

Keywords

  • Time Slice
  • Operational Semantic
  • Deduction System
  • Sequential Composition
  • Parallel Composition

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-30080-9_3
  • Chapter length: 39 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   49.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-30080-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   64.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baeten, J., Bergstra, J.: Real time process algebra. Formal Aspects of Computing 3, 142–188 (1991)

    CrossRef  Google Scholar 

  2. Hennessy, M., Regan, T.: A process algebra for timed systems. Information and Computation 177, 221–239 (1995)

    CrossRef  MathSciNet  Google Scholar 

  3. Moller, F., Tofts, C.: A temporal calculus of communicating systems. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 401–415. Springer, Heidelberg (1990)

    Google Scholar 

  4. Nicollin, X., Sifakis, J.: The algebra of timed processes, ATP: Theory and application. Information and Computation 114, 131–178 (1994)

    MATH  CrossRef  MathSciNet  Google Scholar 

  5. Quemada, J., de Frutos, D., Azcorra, A.: TIC: A TImed calculus. Formal Aspects of Computing 5, 224–252 (1993)

    MATH  CrossRef  Google Scholar 

  6. Bos, S., Reniers, M.: The I2C-bus in discrete-time process algebra. Science of Computer Programming 29, 235–258 (1997)

    CrossRef  Google Scholar 

  7. Schneider, S., Davies, J., Jackson, D., Reed, G., Reed, J., Roscoe, A.: Timed CSP: Theory and practice. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 640–675. Springer, Heidelberg (1992)

    CrossRef  Google Scholar 

  8. Groote, J.: The syntax and semantics of timed μCRL. Technical Report SENR9709, CWI, Amsterdam (1997)

    Google Scholar 

  9. Baeten, J., Bergstra, J.: Discrete time process algebra. Formal Aspects of Computing 8, 188–208 (1996)

    MATH  CrossRef  Google Scholar 

  10. Baeten, J., Bergstra, J.: Discrete time process algebra: absolute time, relative time and parametric time. Fundamenta Informaticae 29, 51–76 (1997)

    MathSciNet  Google Scholar 

  11. Groote, J.: Process Algebra and Structured Operational Semantics. PhD thesis, University of Amsterdam (1991)

    Google Scholar 

  12. Baeten, J., Middelburg, C.: Process Algebra with Timing. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  13. Baeten, J.: Embedding untimed into timed process algebra: the case for explicit termination. Mathematical Structures in Computer Science 13, 589–618 (2003)

    MATH  CrossRef  MathSciNet  Google Scholar 

  14. Baeten, J., Reniers, M.: Explicit termination in timed process algebra with relativetiming. Formal Aspects of Computing (2004) (to appear)

    Google Scholar 

  15. Koymans, C., Vrancken, J.: Extending process algebra with the empty process ε. Technical Report Logic Group Preprint Series 1, University Utrecht, Department of Philosophy (1985)

    Google Scholar 

  16. Baeten, J., Glabbeek, R.v.: Merge and termination in process algebra. In: Nori, K.V. (ed.) FSTTCS 1987. LNCS, vol. 287, pp. 153–172. Springer, Heidelberg (1987)

    Google Scholar 

  17. Vrancken, J.: The algebra of communicating processes with empty process. Theoretical Computer Science 177, 287–328 (1997)

    MATH  CrossRef  MathSciNet  Google Scholar 

  18. Vereijken, J.: Discrete-time process algebra. PhD thesis, Eindhoven University of Technology (1997)

    Google Scholar 

  19. Baeten, J., Vereijken, J.: Discrete-time process algebra with empty process. In: Bruné, M., van Deursen, A., Heering, J. (eds.) Dat is dus heel interessant, CWI. Liber Amicorum dedicated to Paul Klint, pp. 5–24 (1997)

    Google Scholar 

  20. Hoare, C.: Communicating Sequential Processes. International Series in Computer Science. Prentice-Hall International, Englewood Cliffs (1985)

    MATH  Google Scholar 

  21. Bos, V., Kleijn, J.: Formalisation of a production system modelling language: the operational semantics of χ Core. Fundamenta Informaticae 41, 367–392 (2000)

    MATH  Google Scholar 

  22. Reniers, M.: Message Sequence Chart: Syntax and Semantics. PhD thesis, Eindhoven University of Technology (1999)

    Google Scholar 

  23. Groote, J.: Transition system specifications with negative premises. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 332–341. Springer, Heidelberg (1990)

    Google Scholar 

  24. Verhoef, C.: A congruence theorem for structured operational semantics with predicates and negative premises. Nordic Journal of Computing 2, 274–302 (1995)

    MATH  MathSciNet  Google Scholar 

  25. Fokkink, W.: The tyft/tyxt format reduces to tree rules. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 440–453. Springer, Heidelberg (1994)

    Google Scholar 

  26. Baeten, J., Reniers, M.: Termination in timed process algebra. Technical Report CSR 00-13, Eindhoven University of Technology, Department of Computing Science (2000)

    Google Scholar 

  27. Baeten, J., Verhoef, C.: A congruence theorem for structured operational semantics with predicates. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 477–492. Springer, Heidelberg (1993)

    Google Scholar 

  28. Baeten, J., Verhoef, C.: Concrete process algebra. In: Abramsky, S., Gabbay, D.M., Maibaum, T. (eds.) Semantic Modelling. Handbook of Logic in Computer Science, vol. 4, pp. 149–268. Oxford University Press, Oxford (1995)

    Google Scholar 

  29. Baeten, J., Weijland, W.: Process Algebra. Cambridge Tracts in Theoretical Computer Science, vol. 18. Cambridge University Press, Cambridge (1990)

    CrossRef  Google Scholar 

  30. Baeten, J., Basten, T., Reniers, M.: Algebra of Communicating Processes. Cambridge University Press (2004) (to appear)

    Google Scholar 

  31. van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics. Journal of the ACM 43, 555–600 (1996)

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. Vaandrager, F.: Two simple protocols. In: Baeten, J. (ed.) Applications of process algebra. Cambridge Tracts in Theoretical Computer Science, vol. 17, pp. 23–44. Cambridge University Press, Cambridge (1990)

    CrossRef  Google Scholar 

  33. Baeten, J., Middelburg, C., Reniers, M.: A new equivalence for processes with timing. Technical Report CSR 02-10, Eindhoven University of Technology, Department of Computing Science (2002)

    Google Scholar 

  34. Baeten, J., Bergstra, J., Reniers, M.: Discrete time process algebra with silent step. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language, and Interaction: Essays in Honour of Robin Milner. Foundations of Computing Series, pp. 535–569. MIT Press, Cambridge (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Baeten, J.C.M., Reniers, M.A. (2004). Timed Process Algebra (With a Focus on Explicit Termination and Relative-Timing). In: Bernardo, M., Corradini, F. (eds) Formal Methods for the Design of Real-Time Systems. SFM-RT 2004. Lecture Notes in Computer Science, vol 3185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30080-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30080-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23068-7

  • Online ISBN: 978-3-540-30080-9

  • eBook Packages: Springer Book Archive