Abstract
We consider abstraction in probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and non-deterministic choices in their behaviour. We give a set of axioms that completely axiomatises the branching bisimulation for the strictly alternating probabilistic graph model. In addition, several recursive verification rules are identified, allowing us to remove redundant internal activity.
Using the axioms and the verification rules, we have successfully conducted a verification of the Concurrent Alternating Bit Protocol. This is a simple communication protocol, slightly more ‘sophisticated’ than the well-known Alternating Bit Protocol. As channels are lossy, sending continuous streams of data through the channels is a method to overcome this possible loss of data. This instigates a considerable level of parallelism (parallel activities) and as such requires more complex techniques for proving the protocol correct. Using our process algebra we show that after abstraction of internal activity, the protocol behaves as a buffer.
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Andova, S., Baeten, J.C.M., Willemse, T.A.C.: Complete axiomatisation of probabilistic branching bisimulation, CSR (to appear, 2006), preliminary version available at, http://www.cs.ru.nl/timw/completeness.pdf
Andova, S., Willemse, T.A.C.: Branching bisimulation for probabilistic systems: characteristics and decidability. In: Baeten, J.C.M., Corradini, F. (eds.) Theor. Comp. Sci., vol. 356(3), pp. 325–355 (2006); Also appeared as a CSR, University of Twente, TR-CTIT-05-08, 2005
Andova, S., Baeten, J.C.M.: Abstraction in Probabilistic Process Algebra. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 204–219. Springer, Heidelberg (2001)
Andova, S., Baeten, J.C.M.: Alternative composition does not imply non-determinism. Bulletin of the European Association for Theoretical Computer Science 76, 125–127 (2002)
Andova, S.: Probabilistic process algebra, Ph.D. thesis, Eindhoven University of Technology (2002)
Andova, S.: Process Algebra with Probabilistic Choice. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 111–129. Springer, Heidelberg (1999)
Baeten, J.C.M., Bergstra, J.A., Klop, J.W.: On the consistency of Koomen’s fair abstraction rule. Theor. Comp. Sci. 51, 129–176 (1987)
Baeten, J.C.M., Weijland, W.P.: Process algebra. Cambridge University Press, Cambrodge (1990)
Baier, C.: On algorithmic verification methods for probabilistic systems, Habilitation thesis, University of Mannheim (1998)
Bandini, E., Segala, R.: Axiomatizations for Probabilistic Bisimulation. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 370–381. Springer, Heidelberg (2001)
Deng, Y., Palamidessi, C.: Axiomatizations for Probabilistic Finite-State Behaviors. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 110–124. Springer, Heidelberg (2005)
van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. Journal of ACM 43(3), 555–600 (1996)
Hansson, H.: Time and probability in formal design of distributed systems, Ph.D. thesis, DoCS 91/27, University of Uppsala (1991)
Koymans, C.P.J., Mulder, J.C.: A modular approach to protocol verification using process algebra. In: Baeten, J.C.M. (ed.) Applications of Process Algebra. Cambridge Tracts in Theoretical Computer Science, vol. 17, pp. 261–306. Cambridge University Press, Cambridge (1990)
Milner, R.: Communication and concurrency. International Series in Computer Science. Prentice-Hall, Englewood Cliffs (1989)
Philippou, A., Lee, I., Sokolsky, O.: Weak Bisimulation for Probabilistic Systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 334–349. Springer, Heidelberg (2000)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)
Stoelinga, M.: Alea jacta est: Verification of probabilistic, real-time and parametric systems, Ph.D. thesis, Katholieke Universiteit Nijmegen, The Netherlands (2002)
van Wamel, J.: Process Algebra with Language Matching. Theor. Comput. Sci. 177(2), 425–458 (1997)
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Andova, S., Baeten, J.C.M., Willemse, T.A.C. (2006). A Complete Axiomatisation of Branching Bisimulation for Probabilistic Systems with an Application in Protocol Verification. In: Baier, C., Hermanns, H. (eds) CONCUR 2006 – Concurrency Theory. CONCUR 2006. Lecture Notes in Computer Science, vol 4137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11817949_22
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DOI: https://doi.org/10.1007/11817949_22
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