Abstract
In this paper, we develop techniques of action refinement for probabilistic processes within the context of a probabilistic process algebra. A semantic counterpart is carried out in a non-interleaving causality based setting, probabilistic bundle event structures. We show that our refinement notion has the following nice properties: the behaviour of the refined system can be inferred compositionally from the behaviour of the original system and from the behaviour of the systems substituted for actions; the probabilistic extensions of pomset trace equivalence and history preserving bisimulation equivalence are both congruences under the refinement; and with respect to a cpo-based denotational semantics the syntactic and semantic refinements coincide with each other up to the aforementioned equivalence relations when the internal actions are abstracted away.
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References
Abramsky, S., Jung, A., Domain Theory, Handbook of Logic in Computer Science (S. Abramsky and Dov M. Gabbay eds.), Clarendon Press, Volume 3: 1–168, 1994.
Aceto, L, Action Refinement in Process Algebra, Cambridge Univ. Press, 1992.
Bolognesi, T., Brinksma, E., Introduction to the ISO Specification Language LOTOS, Comp. Netw. and ISDN Syst., 14: 25–59, 1987.
Bowman, H., Derrick, J., Extending LOTOS with Time: A True Concurrency Perspective, Lecture Notes in Computer Science, 1231: 383–399, 1997.
Bowman, H., Katoen, J.-P., A True Concurrency Semantics for ET-LOTOS, Proceedings Int. Conference on Applications of Concurrency to System Design, 228–239, 1998.
Brinksma, E., Katoen, J.-P., Langerak, R., and Latella, D., Partial-Order Models for Quantitative Extensions of LOTOS, Computer Networks and ISDN Systems, 30(9/10): 925–950, 1998.
D’Argenio, P. R., Hermanns, H., and Katoen, J.-P., On Generative Parallel Composition, Electronic Notes in Theoretical Computer Science, 22, 1999.
Fecher, H., Majster-Cederbaum, M., and Wu, J., Bundle Event Structures: A Revised Cpo Approach, Information Processing Letters, accepted, 2001.
Fecher, H., Majster-Cederbaum, M., and Wu, J., Refinement of Actions in a Real-Time Process Algebra with a True Concurrency Model, REFINE 2002, accepted, 2002.
van Glabbeek, R., Goltz, U., Refinement of Actions and Equivalence Notions for Concurrent Systems, Acta Informatica, 37: 229–327, 2001.
van Glabbeek, R., Smolka, S. A., and Steffen, B., Reactive, Generative and Stratified Models of Probabilistic Processes, Information and Computation, 121: 59–80, 1995.
van Glabbeek, R., Smolka, S. A., Steffen, B., and Tofts, C. M. N., Reactive, Generative and Stratified Models of Probabilistic Processes, Proc. LICS’90, IEEE-CS Press, 130–141, 1990.
Gorrieri, R., Rensink, A., Action Refinement, Handbook of Process Algebra, Elsevier Science, 1047–1147, 2001.
Hoare, C.A.R., Communicating Sequential Processes, Prentice-Hall, 1985.
Katoen, J.-P., Quantitative and Qualitative Extensions of Event Structures, PhD Thesis, University of Twente, 1996.
Katoen, J.-P., Baier, C., and Latella, D., Metric Semantics for True Concurrent Real Time, Th. Comp. Sci., 254(1-2): 501–542, 2001.
Katoen, J-P., Langerak, R., Latella, D., and Brinksma, E., On Specifying Real-Time Systems in a Causality-Based Setting, in: Formal Techniques in Real-Time and Fault-Tolerant Systems, Lecture Notes in Computer Science, 1135: 385–405, 1996.
Langerak, R., Transformations and Semantics for LOTOS, PhD Thesis, University of Twente, 1992.
Loogn, R., Goltz, U., Modelling Nondeterministic Concurrent Processes with Event Structures, Fund. Inf., 14(1): 39–74, 1991.
Majster-Cederbaum, M., Salger, F., Correctness by Construction: Towards Verification in Hierarchical System Development, Lecture Notes in Computer Science, 1885: 163–180, 2000.
Majster-Cederbaum, M., Salger, F., and Sorea, M., A Priori Verification of Reactive Systems, Proc. FORTE/PSTV 2000, Kluwer Academic Publishers, 35–50, 2000.
Majster-Cederbaum, M., Wu, J., Action Refinement for True Concurrent Real Time, Proc. ICECCS 2001, IEEE Computer Society Press, 58–68, 2001.
Milner, R., Communication and Concurrency, Prentice-Hall, 1989.
Murphy, D., Pitt, D., Real-Timed Concurrent Refineable Behaviours, Lecture Notes in Computer Science, 571: 529–545, 1992.
Zic, J., Time-Constrained Buffer Specifications in CSP+T and Timed CSP, ACM Transactions on Programming and Systems, 16(6): 1661–1674, 1994.
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Fecher, H., Majster-Cederbaum, M., Wu, J. (2002). Action Refinement for Probabilistic Processes with True Concurrency Models. In: Hermanns, H., Segala, R. (eds) Process Algebra and Probabilistic Methods: Performance Modeling and Verification. PAPM-PROBMIV 2002. Lecture Notes in Computer Science, vol 2399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45605-8_6
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DOI: https://doi.org/10.1007/3-540-45605-8_6
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