A hemimetric extension of simulation for semi-markov decision processes

Pedersen, Mathias Ruggaard and Bacci, Giorgio and Larsen, Kim Guldstrand and Mardare, Radu; McIver, Annabelle and Horvath, Andras, eds. (2018) A hemimetric extension of simulation for semi-markov decision processes. In: Quantitative Evaluation of Systems - 15th International Conference, QEST 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer-Verlag, CHN, pp. 339-355. ISBN 9783319991535 (https://doi.org/10.1007/978-3-319-99154-2_21)

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Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line. In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7), where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic.