Abstract
Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs, a.k.a. probabilistic automata). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] define a probabilistic Hennessy-Milner logic interpreted over distributions, whose logical equivalence/preorder when restricted to Dirac distributions coincide with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between distributions in terms of a notion of bisimulation/simulation defined on a LTS of probability distributions (DLTS). We show that the standard spectrum of behavioral relations on nonprobabilistic LTSs as well as its logical characterization in terms of Hennessy-Milner logic scales to the probabilistic setting when considering DLTSs.
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References
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc. 4th ACM POPL (1977)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Proc. 6th ACM POPL, pp. 269–282 (1979)
Crafa, S., Ranzato, F.: Probabilistic bisimulation and simulation algorithms by abstract interpretation. In: Aceto, L. (ed.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 295–306. Springer, Heidelberg (2011)
Deng, Y., van Glabbeek, R.: Characterising probabilistic processes logically. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 278–293. Springer, Heidelberg (2010)
Deng, Y., van Glabbeek, R., Hennessy, M., Morgan, C.: Characterising testing preorders for finite probabilistic processes. Logical Methods in Computer Science 4(4) (2008)
Desharnais, J.: Labelled Markov Processes. PhD thesis, McGill Univ. (1999)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Weak bisimulation is sound and complete for PCTL*. In: Brim, L., Jančar, P., Křetínský, M., Kučera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 355–370. Springer, Heidelberg (2002)
van Glabbeek, R.J.: The linear time – branching time spectrum I; the semantics of concrete, sequential processes. In: Handbook of Process Algebra, ch. 1, pp. 3–99. Elsevier, Amsterdam (2001)
van Glabbeek, R.J., Smolka, S., Steffen, B., Tofts, C.: Reactive, generative and stratified models for probabilistic processes. In: Proc. IEEE LICS 1990, pp. 130–141 (1990)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)
Hermanns, H., Parma, A., Segala, R., Wachter, B., Zhang, L.: Probabilistic logical characterization. Information and Computation 209(2), 154–172 (2011)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)
Parma, A., Segala, R.: Logical characterizations of bisimulations for discrete probabilistic systems. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 287–301. Springer, Heidelberg (2007)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT (1995)
Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. Nordic J. of Computing 2(2), 250–273 (1995)
Stoelinga, M.: Alea Jacta Est: Verification of Probabilistic, Real-Time and Parametric Systems. PhD thesis, University of Nijmegen, The Netherlands (2002)
Zhang, L., Hermanns, H., Eisenbrand, F., Jansen, D.N.: Flow faster: efficient decision algorithms for probabilistic simulations. Logical Methods in Computer Science 4(4) (2008)
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Crafa, S., Ranzato, F. (2011). A Spectrum of Behavioral Relations over LTSs on Probability Distributions. In: Katoen, JP., König, B. (eds) CONCUR 2011 – Concurrency Theory. CONCUR 2011. Lecture Notes in Computer Science, vol 6901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23217-6_9
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DOI: https://doi.org/10.1007/978-3-642-23217-6_9
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