Abstract
We consider a simple divergence-free language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language. Following the methodology introduced by de Bakker & Zucker we give denotational semantics to this language by means of a complete metric space of (deterministic) probabilistic trees defined in terms of the powerdomain of closed sets. This new metric, although not an ultra-metric, nevertheless specialises to the metric of de Bakker & Zucker. Our semantic domain admits a full abstraction result with respect to probabilistic bisimulation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
P.H.M.America and J.J.M.M.Rutten. Solving reflexive domain equations in a category of complete metric spaces, JCSS, 39, no.3, 1989.
J.C.M.Baeten, J.A.Bergstra and S.A.Smolka. Axiomatising probabilistic processes: ACP with generative probability, Proc. Concur'92, LNCS, 630, Springer, 1992.
C.Baier and M.Kwiatkowska. Domain equations for probabilistic processes, preprint.
I.Christoff. Testing equivalences and fully abstract models for probabilistic processes, Proc. Concur'90, LNCS, 458, Springer, 1990.
J.W.de Bakker and J.I.Zucker. Processes and the denotational semantics of concurrency, Information and Control, 1/2, 1984.
A.Giacalone, C.-C.Jou and S.A.Smolka. Algebraic reasoning for probabilistic concurrent systems, In Proc. Programming Concepts and Methods, IFIP, 1990.
M.Große-Rhode and H.Ehrig. Transformation of combined data type and process specifications using projection algebras, LNCS, 430, Springer, 1989.
C.A.Hoare. Communicating sequential processes, Prentice Hall, 1985.
C.Jones. Probabilistic non-determinism, PhD Thesis, University of Edinburgh, 1990.
B.Jonsson and K.G.Larsen. Specification and refinement of probabilistic processes, Proc. IEEE Logic in Computer Science (LICS), 1991.
B.Jonsson and Wang Yi. Compositional testing preorders for probabilistic processes, Proc. IEEE Logic in Computer Science (LICS), 1995.
C.-C.Jou and S.Smolka. Equivalences, congruences and complete axiomatizations for probabilistic processes, Proc. Concur'90, LNCS, 458, Springer, 1990.
D.Kozen. Semantics of probabilistic programs, Proc. IEEE Symposium on Foundations of Computer Science (FOCS), 1979.
K.G.Larsen and A.Skou. Bisimulation through probabilistic testing, Information and Computation, 94, 1991.
K.G.Larsen and A.Skou. Compositional verification of probabilistic processes, Proc. Concur'92, LNCS, 630, Springer, 1992.
R.Milner. Calculi for synchrony and asynchrony, TCS, 25(3), 1983.
R.Milner. Communication and concurrency, Prentice Hall, 1989.
K.Seidel. Probabilistic communicating processes, TCS, 152, 1995.
C.Tofts. A synchronous calculus of relative frequency, Proc. Concur'90, LNCS, 458, Springer, 1990.
R.J.van Glabbeek, S.A.Smolka, B.Steffen and C.Tofts. Reactive, generative and stratified models of probabilistic processes, Proc. Concur'92, LNCS, 630, Springer, 1992.
S.Yuen, R.Cleaveland, Z.Dayar and S.A.Smolka. Fully abstract characterizations of testing preorders for probabilistic processes, Proc. Concur'94, LNCS, 836, Springer, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kwiatkowska, M., Norman, G. (1996). Probabilistic metric semantics for a simple language with recursion. In: Penczek, W., Szałas, A. (eds) Mathematical Foundations of Computer Science 1996. MFCS 1996. Lecture Notes in Computer Science, vol 1113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61550-4_167
Download citation
DOI: https://doi.org/10.1007/3-540-61550-4_167
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61550-7
Online ISBN: 978-3-540-70597-0
eBook Packages: Springer Book Archive