Abstract
Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of “interesting” properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Supported by NSF grant CCR-89-15206, and CCR-92-25124, by DARPA contracts N00014-89-J-1988 and N00014-92-J-4033, and by ONR contract N00014-91-J-1046.
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References
J. Aspnes and M.P. Herlihy. Fast randomized consensus using shared memory. Journal of Algorithms, 15(1):441–460, September 1990.
M. Ben-Or. Another advantage of free choice: completely asynchronous agreement protocols. In Proceedings of the 2 nd PODC, August 1983.
I. Christoff. Testing equivalences for probabilistic processes. Technical Report DoCS 90/22, Ph.D. Thesis, Department of Computer Science, Uppsala University, Sweden, 1990.
M. Fischer and L. Zuck. Reasoning about uncertainty in fault tolerant distributed systems. In Proceedings of the Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, LNCS 331, pages 142–158, 1988.
R.J. van Glabbeek, S.A. Smolka, B. Steffen, and C.M.N. Tofts. Reactive, generative, and stratified models of probabilistic processes. In Proceedings 5 th LICS, pages 130–141. IEEE Computer Society Press, 1990.
R.J. van Glabbeek and W.P. Weijland. Branching time and abstraction in bisimulation semantics (extended abstract). In Information Processing 89, pages 613–618. North-Holland, 1989. Full version available as Report CS-R9120, CWI, Amsterdam, 1991.
H. Hansson. Time and Probability in Formal Design of Distributed Systems. PhD thesis, Department of Computer Science, Uppsala University, 1991.
M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.
C.A.R. Hoare. Communicating Sequential Processes. Prentice-Hall International, 1985.
B. Jonsson. Simulations between specifications of distributed systems. In Proceedings CONCUR 91, LNCS 527, pages 346–360, 1991.
B. Jonsson and K. G. Larsen. Specification and refinement of probabilistic processes. In Proceedings of the 6th LICS, July 1991.
E. Kushilevitz and M. Rabin. Randomized mutual exclusion algorithms revisited. In Proceedings of the 11th PODC, pages 275–284, 1992.
K. G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94(1):1–28, September 1992.
D. Lehmann and M. Rabin. On the advantage of free choice: a symmetric and fully distributed solution to the dining philosophers problem. In Proceedings of the 8th POPL pages 133–138, January 1981.
N.A. Lynch and M.R. Tuttle. Hierarchical correctness proofs for distributed algorithms. In Proceedings of the 6th PODC, pages 137–151, Vancouver, Canada, August 1987. A full version is available as MIT Technical Report MIT/LCS/TR-387.
N.A. Lynch and F.W. Vaandrager. Forward and backward simulations for timing-based systems. In Proceedings of the REX Workshop “Real-Time: Theory in Practice”, LNCS 600, pages 397–446, 1991.
R. Milner. Communication and Concurrency. Prentice-Hall International, 1989.
A. Pnueli. The temporal semantics of concurrent programs. TCS, 13:45–60, 1982.
A. Pnueli and L. Zuck. Verification of multiprocess probabilistic protocols. Distributed Computing, 1(1):53–72, 1986.
K. Seidel. Probabilistic communicating processes. Technical Report PRG-102, Ph.D. Thesis, Programming Research Group, Oxford University Computing Laboratory, 1992.
M. Y. Vardi. Automatic verification of probabilistic concurrent finite-state programs. In Proceedings of 26th FOCS, pages 327–338, Portland, OR, 1985.
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© 1994 Springer-Verlag
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Segala, R., Lynch, N. (1994). Probabilistic simulations for probabilistic processes. In: Jonsson, B., Parrow, J. (eds) CONCUR '94: Concurrency Theory. Lecture Notes in Computer Science, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015027
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DOI: https://doi.org/10.1007/BFb0015027
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