Abstract
In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics defined in [19].
Research partially supported by the CICYT projects TIC 94-0851-C02-02 and TIC 97-0669-C03-01.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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. Information and Computation, 121(2):234–255, 1995.
C. Baier and H. Hermanns. Weak bisimulation for fully probabilistic processes. In Computer Aided Verification’97, LNCS 1254, pages 119–130. Springer, 1997.
I. Christoff. Testing equivalences and fully abstract models for probabilistic processes. In CONCUR’90, LNCS 458, pages 126–140. Springer, 1990.
R. Cleaveland, I. Lee, P. Lewis, and S.A. Smolka. A theory of testing for soft real-time processes. In 8th International Conference on Software Engineering and Knowledge Engineering, 1996.
R. Cleaveland, S.A. Smolka, and A.E. Zwarico. Testing preorders for probabilistic processes. In 19th ICALP, LNCS 623, pages 708–719. Springer, 1992.
F. Cuartero, D. de Frutos, and V. Valero. A sound and complete proof system for probabilistic processes. In 4th International AMAST Workshop on Real-Time Systems, Concurrent and Distributed Software, LNCS 1231, pages 340–352. Springer, 1997.
P.R. D’Argenio, H. Hermanns, and J.-P. Katoen. On generative parallel composition. In Workshop on Probabilistic Methods in Verification, PROBMIV’98, pages 105–121, 1998.
R. de Nicola and M.C.B. Hennessy. Testing equivalences for processes. Theoretical Computer Science, 34:83–133, 1984.
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. North Holland, 1990.
C. Gregorio, L. Llana, M. Núñez, and P. Palao. Testing semantics for a probabilistic-timed process algebra. In 4th International AMAST Workshop on Real-Time Systems, Concurrent, and Distributed Software, LNCS 1231, pages 353–367. Springer, 1997.
C. Gregorio and M. Núñez. Denotational semantics for probabilistic refusal testing. In Workshop on Probabilistic Methods in Verification, PROBMIV’98, pages 123–137, 1998.
M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.
C.-C. Jou and S.A. Smolka. Equivalences, congruences and complete axiomatizations for probabilistic processes. In CONCUR’90, LNCS 458, pages 367–383. Springer, 1990.
K. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94(1):1–28, 1991.
K.G. Larsen and A. Skou. Compositional verification of probabilistic processes. In CONCUR’92, LNCS 630, pages 456–471. Springer, 1992.
G. Lowe. Probabilistic and prioritized models of timed CSP. Theoretical Computer Science, 138:315–352, 1995.
M. Núñez. Semánticas de Pruebas para Álgebras de Procesos Probabilśticos. PhD thesis, Universidad Complutense de Madrid, 1996.
M. Núñez and D. de Frutos. Testing semantics for probabilistic LOTOS. In Formal Description Techniques VIII, pages 365–380. Chapman & Hall, 1995.
M. Núñez, D. de Frutos, and L. Llana. Acceptance trees for probabilistic processes. In CONCUR’95, LNCS 962, pages 249–263. Springer, 1995.
E.W. Stark and S.A. Smolka. A complete axiom system for finite-state probabilistic processes, 1996.
C. Tofts. A synchronous calculus of relative frequency. In CONCUR’90, LNCS 458, pages 467–480. Springer, 1990.
R. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121(1):59–80, 1995.
W. Yi and K.G. Larsen. Testing probabilistic and nondeterministic processes. In Protocol Specification, Testing and Verification XII, pages 47–61. North Holland, 1992.
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. Springer, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Núñez, M. (1999). An Axiomatization of Probabilistic Testing. In: Katoen, JP. (eds) Formal Methods for Real-Time and Probabilistic Systems. ARTS 1999. Lecture Notes in Computer Science, vol 1601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48778-6_8
Download citation
DOI: https://doi.org/10.1007/3-540-48778-6_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66010-1
Online ISBN: 978-3-540-48778-4
eBook Packages: Springer Book Archive