Abstract
Probabilistic automata are a central model for concurrent systems exhibiting random phenomena. This paper presents, in a uniform setting, efficient decision algorithms for strong simulation on probabilistic automata, but with subtly different results. The algorithm for strong probabilistic simulation is shown to be of polynomial complexity via a reduction to LP problem, while the algorithm for strong simulation has complexity \(\mathcal{O}(m^2n)\). The former relation allows for convex combinations of transitions in the definition and is thus less discriminative than the latter. As a byproduct, we obtain minimisation algorithms with respect to strong simulation equivalences and – for Markov decision processes – also to strong bisimulation equivalences. When extending these algorithms to the continuous-time setting, we retain same complexities for both strong simulation and strong probabilistic simulations.
This work is supported by the NWO-DFG bilateral project VOSS and by the DFG as part of the Transregional Collaborative Research Center SFB/TR 14 AVACS.
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References
Baier, C.: On Algorithmic Verification Methods for Probabilistic Systems, Habilitations-schrift zur Erlangung der venia legendi der Fakultät für Mathematik and Informatik, Universität Mannheim (1998)
Baier, C., Engelen, B., Majster-Cederbaum, M.E.: Deciding bisimilarity and similarity for probabilistic processes. J. Comput. Syst. Sci. 60(1), 187–231 (2000)
Baier, C., Hermanns, H., Katoen, J.-P., Haverkort, B.R.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time markov decision processes. Theor. Comput. Sci. 345(1), 2–26 (2005)
Baier, C., Katoen, J.-P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for markov chains. Inf. Comput 200(2), 149–214 (2005)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Cattani, S., Segala, R.: Decision algorithms for probabilistic bisimulation. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 371–385. Springer, Heidelberg (2002)
Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18(1), 30–55 (1989)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM 35(4), 921–940 (1988)
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: LICS, pp. 266–277 (1991)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Chichester (1994)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nord. J. Comput. 2(2), 250–273 (1995)
Wolovick, N., Johr, S.: A characterization of meaningful schedulers for continuous-time markov decision processes. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 352–367. Springer, Heidelberg (2006)
Zhang, L., Hermanns, H., Eisenbrand, F., Jansen, D.N.: Flow faster: Efficient decision algorithms for probabilistic simulations. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 155–169. Springer, Heidelberg (2007)
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Zhang, L., Hermanns, H. (2007). Deciding Simulations on Probabilistic Automata . In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds) Automated Technology for Verification and Analysis. ATVA 2007. Lecture Notes in Computer Science, vol 4762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75596-8_16
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DOI: https://doi.org/10.1007/978-3-540-75596-8_16
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