A synchronous calculus of relative frequency

  • Chris Tofts
Selected Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 458)


We present a weighted synchronous calculus that can be interpreted as reasoning over probabilistic processes [LS89,SST89,GSST90]. The abstraction from absolute weight to relative frequency is obtained semantically. We also add a notion of dominance which can be interpreted as priority. This notion is shown to be dual to that of “zero probability” [SST89,GSST90] and can be used to construct arbitrary priority structures. Finally, an equational system for reasoning about the weighted processes is presented.


Relative Frequency Operational Semantic Markov Chain Model Axiom System Operational Rule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

8 Bibliography

  1. [BBK86]
    J. Baeten, J. Bergstra and J. Klop, Syntax and defining equations for an interrupt mechanism in process algebra, Fundamenta Informatica IX, pp 127–168, 1986Google Scholar
  2. [CH88]
    R. Cleveland and M. Hennessey, Priorites in Process Algebras, proceedings LICS 1988.Google Scholar
  3. [GJS90]
    A. Giaclone, C.-C. Jou, and S. A. Smolka, Algebraic reasoning for probabilistic concurrent systems, proceedings of working conference on programming concepts and methods IFIP TC 2, 1990.Google Scholar
  4. [GSST90]
    R. van Glabbek, S. A. Smolka, B. Steffen and C. Tofts, Reactive, Generative and Stratified Models of Probabilistic Processes, proceedings LICS 1990.Google Scholar
  5. [JP89]
    C. Jones and G. D. Plotkin, A probabilistic powerdomain of evaluations, proceedings LICS 1989.Google Scholar
  6. [Kei]
    J. Keilson, Markov Chain Models — Rarity and exponentiality, Applied Mathematical Sciences 28, Springer Verlag.Google Scholar
  7. [LS89]
    K. G. Larsen and A. Skou. Bisimulation through probabilistic testing. proceedings POPL 1989.Google Scholar
  8. [Mil83]
    R. Milner, Calculi for Synchrony and Asynchrony, Theoretical Computer Science 25(3), pp 267–310, 1983.Google Scholar
  9. [Mil89]
    R. Milner, Communication and Concurrency, Prentice Hall, 1989.Google Scholar
  10. [MT89]
    F. Moller and C.Tofts, a Temporal Calculus of Communicating Systems, LFCS-89-104, University of Edinburgh.Google Scholar
  11. [Par81]
    D. Park, Concurrency and Automata on infinite sequences, Springer LNCS 104.Google Scholar
  12. [Plo81]
    G. D. Plotkin, A structured approach to operational semantics. Technical report Daimi Fn-19, Computer Science Department, Aarhus University. 1981Google Scholar
  13. [Rab76]
    M. Rabin, Probabilistic algorithmns, Algorithmns and Complexity, recent results and new directions, J. Traub ed Academic press, New York, 1976 pp 21–39.Google Scholar
  14. [SST89]
    S. Smolka, B. Steffen and C. Tofts, unpublished notes. Working title, Probability + Restriction ⇒ priority.Google Scholar
  15. [Tof89]
    C. Tofts, Timing Concurrent Processes, LFCS-89-103, University of Edinburgh.Google Scholar
  16. [Tof90a]
    C. Tofts, Proof Methods and Pragmatics for Parallel Programming, Thesis in examination.Google Scholar
  17. [Tof90b]
    C. Tofts, Relative Frequency in a Synchronous Calculus, LFCS-90-108, University of Edinburgh.Google Scholar
  18. [Wel83]
    D. Welsh, Randomised algorithmns, Discrete applied mathematics 5, 1983 pp 133–145.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Chris Tofts
    • 1
  1. 1.Laboratory for the Foundations of Computer Science Department of Computer ScienceEdinburgh UniversityUK

Personalised recommendations