Abstract
Jones and Plotkin give a general construction for forming a probabilistic powerdomain over any directed-complete partial order [Jon90, JoP89]. We apply their technique to the failures/divergences semantic model for Communicating Sequential Processes [Hoa85].
The resulting probabilistic model supports a new binary operator, probabilistic choice, and retains all operators of CSP including its two existing forms of choice. An advantage of using the general construction is that it is easy to see which CSP identities remain true in the probabilistic model. A surprising consequence however is that probabilistic choice distributes through all other operators; such algebraic mobility means that the syntactic position of the choice operator gives little information about when the choice actually must occur. That in turn leads to some interesting interaction between probability and nondeterminism.
A simple communications protocol is used to illustrate the probabilistic algebra, and several suggestions are made for accommodating and controlling nondeterminism when probability is present.
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Baeten, J.C.M. and Bergstra, J.A.: Process algebra with partial choice. InCONCUR 94, number 836 in LNCS, pages 465–480. Springer Verlag, 1994.
Baeten, J.C.M., Bergstra, J.A. and Smolka, S.A.: Axiomatising probabilistic processes: ACP with generative probabilities. InCONCUR 92, number 630 in LNCS, pages 472–485. Springer Verlag, 1992.
Baeten, J.C.M. and Weijland, W.P.:Process Algebra, volume 18 ofCambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1990.
Dijkstra, E.W.:A Discipline of Programming. Prentice Hall International, Englewood Cliffs, 1976.
Nicola, M. de and Hennessy, M.: Testing equivalence for processes.Theoretical Computer Science, 34, 1984.
RAISE Language Group.The RAISE Specification Language. Prentice-Hall, 1992.
Hoare, C.A.R.:Communicating Sequential Processes. Prentice Hall International, 1985.
Jones, C.: Probabilistic nondeterminism. Monograph ECS-LFCS-90-105, Edinburgh University, 1990. (PhD Thesis).
Jones, C. and Plotkin, G.: A probabilistic powerdomain of evaluations. InProceedings of the IEEE 4th Annual Symposium on Logic in Computer Science, pages 186–195. Computer Society Press, 1989.
Lowe, G.: Representing nondeterministic and probabilistic behaviour in reactive processes. Submitted for publication.
Lowe, G.: Probabilities and priorities in timed CSP. Technical Monograph PRG-111, Oxford University Computing Laboratory, 1993. (DPhil Thesis).
Larsen, K.G. and Skou, A.: Bisimulation through probabilistic testing. InProceedings of 16th ACM Symposium on Principles of Programming Languages, Austin, Texas, 1989.
Milner, R.:Communication and Concurrency. Prentice Hall International, 1989.
McIver, A., Morgan, C., Seidel, K. and Sanders, J.W.: A power construction for nondeterminism over probability. In preparation.
Morgan, C., McIver, A., Seidel, K. and Sanders, J.W.: Argument duplication in probabilistic CSP. Technical Report PRG-TR-11-95, Programming Research Group, April 1995.
Pnueli, A.: Linear and branching structure in the semantics and logics of reactive systems. InProceedings of 12th International Colloquium on Automata, Languages and Programming, number 458 in LNCS. Springer Verlag, 1985.
Seidel, K.: Probabilistic communicating processes. Technical Monograph PRG-102, Oxford University, 1992. (DPhil Thesis).
Smyth, M.B.: Power domains and predicate transformers: a topological view. InAutomata, Languages and Programming 10th Colloquium, Barcelona, Spain, number 154 in LNCS. Springer Verlag, 1983.
Tanenbaum, A.S.:Computer Networks. Prentice-Hall, second edition, 1988.
Glabbeek, R.J. van, Smolka, S.A., Steffen, B. and Tofts, C.: Reactive, generative and stratified models of probabilistic processes. InIEEE Symposium on Logic in Computer Science, Philadelphia, PA, USA, June 1990.
Yi, W. and Larsen, K.G.: Testing probabilistic and nondeterministic processes. InProceedings of 12th IFIP International Symposium on Protocol Specification, Testing and Verification, Florida, USA, 1992.
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All authors are members of the Programming Research Group; McIver and Seidel are supported by the EPSRC.0
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Morgan, C., McIver, A., Seidel, K. et al. Refinement-oriented probability for CSP. Formal Aspects of Computing 8, 617–647 (1996). https://doi.org/10.1007/BF01213492
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DOI: https://doi.org/10.1007/BF01213492