Abstract
In this paper we study the extension of classical testing theory to a probabilistic process algebra. We consider a generative interpretation of probabilities for a language with two choice operators (one internal and the other external), which are annotated with a probability p ε (0, 1). We define a testing semantics for our language, and we write P pass p T to denote that the process P passes the test T with a probability p. We also give a set of essential tests which has the same strength as the full family of tests.Next we give an alternative characterization of the testing semantics, based on the idea of acceptance sets, and we prove that the new equivalence is equal to the testing equivalence. Finally, we present a fully abstract denotational semantics based on acceptance trees.
Research partially supported by the CICYT project TIC 94-0851-C02-02
Preview
Unable to display preview. Download preview PDF.
References
J.C.M. Baeten, J.A. Bergstra, and S.A. Smolka. Axiomatizing probabilistic processes: ACP with generative probabilities. In CONCUR'92, LNCS 630, pages 472–485, 1992.
I. Christoff. Testing equivalences and fully abstract models for probabilistic processes. In CONCUR'90, LNCS 458, pages 126–140, 1990.
R. Cleaveland, S.A. Smolka, and A.E. Zwarico. Testing preorders for probabilistic processes. In 19 th ICALP, LNCS 623, pages 708–719, 1992.
F. Cuartero. CSP probabilístico (PCSP). Un modelo probabilístico de procesos concurrentes. PhD thesis, Universidad Complutense de Madrid, 1993.
R. de Nicola and M. Hennessy. CCS without τ's. In TAPSOFT'87, LNCS 249, pages 138–152, 1987.
A. Giacalone, C.-C. Jou, and S.A. Smolka. Algebraic reasoning for probabilistic concurrent systems. In Proceedings of Working Conference on Programming Concepts and Methods, IFIP TC 2, 1990.
M. Hennessy. Acceptance trees. Journal of the ACM, 32(4):896–928, 1985.
M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.
H. Hansson and B. Jonsson. A calculus for communicating systems with time and probabilities. In 11th IEEE Real-Time Systems Symposium, pages 278–287, 1990.
B. Jonsson and W. Yi. Compositional testing preorders for probabilistic processes. In 10th IEEE Symposium on Logic In Computer Science, 1995.
G. Lowe. Probabilistic and prioritized models of timed CSP. Theoretical Computer Science, 138:315–352, 1995.
K.G. Larsen and A. Skou. Compositional verification of probabilistic processes. In CONCUR'92, LNCS 630, pages 456–471, 1992.
K. Seidel. Probabilistic Communicating Processes. PhD thesis, Oxford University, 1992.
S.A. Smolka and B. Steffen. Priority as extremal probability. In CONCUR'90, LNCS 458, pages 456–466, 1990.
R. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Tofts. Reactive, generative, and stratified models of probabilistic processes. In 5th IEEE Symposium on Logic In Computer Science, pages 130–141, 1990.
S.-H. Wu, S.A. Smolka, and E.W. Stark. Composition and behaviors of probabilistic I/O automata. In CONCUR'94, LNCS 836, pages 513–528, 1994.
S. Yuen, R. Cleaveland, Z. Dayar, and S.A. Smolka. Fully abstract characterizations of testing preorders for probabilistic processes. In CONCUR'94, LNCS 836, pages 497–512, 1994.
W. Yi and K.G. Larsen. Testing probabilistic and nondeterministic processes. In PSTV XII, pages 47–61, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Núñez, M., de Frutos, D., Llana, L. (1995). Acceptance trees for probabilistic processes. In: Lee, I., Smolka, S.A. (eds) CONCUR '95: Concurrency Theory. CONCUR 1995. Lecture Notes in Computer Science, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60218-6_18
Download citation
DOI: https://doi.org/10.1007/3-540-60218-6_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60218-7
Online ISBN: 978-3-540-44738-2
eBook Packages: Springer Book Archive