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Axiomatising real-timed processes

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Mathematical Foundations of Programming Semantics (MFPS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 802))

Abstract

In this paper, we present a relativised compositional proof system for real-timed processes. The proof system allows us to derive statements of the form A ⊢ E = F, where processes E, F may contain free time variables and A is a formula of the first order theory of time domain. The formula A ⊢ E = F means that A is a condition for process E to be bisimilar to process F. The proof system is sound and is independent of the choice of time domain, allowing time to be discrete or dense. It is complete for finite terms, i.e. terms without recursion, over dense time domains. It is also shown complete for a sublanguage over discrete time domains. We discuss how to restrict occurrences of time variables to obtain the sublanguage. We finally discuss extensions of the proof system for recursively defined processes.

The author is supported by grant GR/G54399 of the Science and Engineering Research Council of the UK. Most of the work was done when the author was in LFCS, University of Edinburgh.

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References

  1. S. Anderson, L. Chen & F. Moller, Observing Causality in Real-Timed Calculi, Preliminary Draft, LFCS, University of Edinburgh, 1992

    Google Scholar 

  2. J.C.M. Baeten & J.A. Bergstra, Real Time Process Algebra, Formal Aspects of Computing, Vol 3, No 2, pp142–188, 1991

    Google Scholar 

  3. J.A. Bergstra & J.W. Klop, Algebra of Communicating Processes with Abstraction, Theoretical Computer Science 37, pp 77–12, 1985

    Google Scholar 

  4. L. Chen, Specification and Verification of Real-Time Systems, Note, 1991

    Google Scholar 

  5. L. Chen, Decidability and Completeness in Real-Time Processes, Technical Report ECS-LFCS-91-185, Edinburgh University, 1991

    Google Scholar 

  6. L. Chen, An Interleaving Model for Real-Time Systems, Proc. of Logical Foundations of Computer Science, Lecture Notes in Computer Science 620, pp 81–92, 1992

    Google Scholar 

  7. L. Chen, Timed Processes: Models, Axioms and Decidability, Ph.D Thesis, University of Edinburgh, 1992

    Google Scholar 

  8. L. Chen, A Model for Real-Time Process Algebras, Proc. MFCS'93, Lecture Notes in Computer Science, 1993

    Google Scholar 

  9. L. Chen, S. Anderson & F. Moller, A Timed Calculus of Communicating System, Technical Report ECS-LFCS-90-127, University of Edinburgh, 1990

    Google Scholar 

  10. P. Degano, R. De Nicola & U. Montanari, Partial Orderings Descriptions and Observations of Nondeterministics Concurrent Processes, Lecture Notes in Computer Science 354, pp 438–466, 1989

    Google Scholar 

  11. M. Hennessy, Axiomatising Finite Concurrent Processes, SIAM J. Comput. Vol 17, No 5, pp 997–1017, 1988

    Google Scholar 

  12. M. Hennessy, A Proof System for Communicating Processes with Value-Passing, Formal Aspects of Computing, Vol. 3, No. 4, pp 346–366, 1991

    Google Scholar 

  13. C.A.R. Hoare, Communicating Sequential Processes, Prentice-Hall international, 1985

    Google Scholar 

  14. A.S. Klusener, Completeness in Real Time Process Algebra, Proceedings of CONCUR'91, Lecture Notes in Computer Science 527, pp 96–110, 1991

    Google Scholar 

  15. R. Milner, A Calculus of Communicating systems, Lecture Notes in Computer Science 92, Springer-verlag, 1980

    Google Scholar 

  16. R. Milner, Communication and Concurrency, Prentice-Hall international, 1989

    Google Scholar 

  17. F. Moller & C. Tofts, A Temporal Calculus of Communicating System, Lecture Notes in Computer Science 458, pp 401–415, 1990

    Google Scholar 

  18. R. Reed & A. W. Roscoe, A Timed Model for Communicating Sequential Processes, Theoretical Computer Science, 58, pp 249–261, 1988

    Google Scholar 

  19. Y. Wang, CCS + Time = an Interleaving Model for Real Time Systems, Proc. of ICALP'91, Lecture Notes in Computer Science, 1991

    Google Scholar 

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Author information

Authors and Affiliations

  1. Centre for Communications Research, University of Bristol Queen's Building, BS8 1TR, Bristol, Great Britain

    Liang Chen

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  1. Liang Chen
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Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1994 Springer-Verlag Berlin Heidelberg

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Chen, L. (1994). Axiomatising real-timed processes. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_10

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  • DOI: https://doi.org/10.1007/3-540-58027-1_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58027-0

  • Online ISBN: 978-3-540-48419-6

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