Formal Aspects of Computing

, Volume 5, Issue 6, pp 530–553 | Cite as

Recursion induction for real-time processes

  • Jim Davies
  • Steve Schneider


The theory of timed Communicating Sequential Processes is a mathematical approach to the design and analysis of timed distributed systems. This paper extends the language of timed CSP to include a general treatment of recursion. A semantics for mutual recursion is introduced, together with a sufficient condition for the necessary fixpoint to be unique. The resulting language has the familiar unwinding property of process algebra, and exhibits a number of useful algebraic identities. A theory of recursion induction is formulated, and a simple example is presented to illustrate its use.


Timed CSP Process algebra Recursion induction Fixed point theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BaB91]
    Baeten, J. C. M. and Bergstra, J. A.: Real time process algebra.Formal Aspects of Computing 3:142–188 (1991).Google Scholar
  2. [BBK87]
    Baeten, J. C. M., Bergstra, J. A. and Klop, J. W.: On the consistency of Koomen's fair abstraction rule.Theoretical Computer Science 51 (1987).Google Scholar
  3. [BKP85]
    Barringer, H., Kuiper R. and Pnueli, A.: A really abstract concurrent model and its temporal logic.Proceedings of the 13th ACM Symposium on the Principles of Programming Languages, 1985.Google Scholar
  4. [Bri92]
    Brinksma, E.: On the uniqueness of fixpoints modulo observation congruence.Proceedings of CONCUR 92, Springer LNCS 630, 1992.Google Scholar
  5. [DaS89]
    Davies, J. W. and Schneider, S. A.:Factorising proofs in timed CSP. Proceedings of the Fifth Conference on the Mathematical Foundations of Programming Semantics, Springer LNCS 439, 1989.Google Scholar
  6. [Dav91]
    Davies, J. W.:Specification and proof in real-time systems. Programming Research Group Technical Monograph PRG-93, Oxford University, 1991.Google Scholar
  7. [End77]
    Enderton, H. B.:Elements of Set Theory. Academic Press, 1977.Google Scholar
  8. [HeR90]
    Hennessy, M. and Regan, T.:A Temporal Process Algebra. Technical Report 2-90, University of Sussex, 1990.Google Scholar
  9. [Hoa85]
    Hoare, C. A. R.:Communicating Sequential Processes. Prentice-Hall International, 1985.Google Scholar
  10. [MoT90]
    Moller, F. and Tofts, C.:A temporal calculus of communicating systems. Proceedings of CONCUR 90, Springer LNCS 458, 1990.Google Scholar
  11. [NRS90]
    Nicollin, X., Richier, J.-L., Sifakis, J. and Voiron, J.:ATP: an algebra for timed processes. Proceedings of the IFIP Working Conference on Programming Concepts and Methods, 1990.Google Scholar
  12. [Ree88]
    Reed, G. M.:A uniform mathematical theory for real-time distributed computing. Oxford University D.Phil thesis, 1988.Google Scholar
  13. [ReR86]
    Reed, G. M. and Roscoe, A. W.:A timed model for communicating sequential processes. Proceedings of ICALP'86, Springer LNCS 226 314–323, 1986,Theoretical Computer Science 58; 249–261, (1988).Google Scholar
  14. [Ros82]
    Roscoe, A. W.: Amathematical theory of communicating processes. Oxford University D.Phil thesis, 1982.Google Scholar
  15. [Sch90]
    Schneider, S. A.:Correctness and communication in real-time systems. Programming Research Group Technical Monograph PRG-84, Oxford University, 1990.Google Scholar
  16. [Sut75]
    Sutherland, W. A.:Introduction to Metric and Topological Spaces. Oxford University Press, 1975.Google Scholar
  17. [Wan91]
    Wang Yi.:A calculus of real time systems. Ph.D thesis, Chalmers University of Technology, 1991.Google Scholar

Copyright information

© BCS 1993

Authors and Affiliations

  • Jim Davies
    • 1
  • Steve Schneider
    • 1
  1. 1.Programming Research GroupOxford UniversityOxfordUK

Personalised recommendations