A Hemimetric Extension of Simulation for Semi-Markov Decision Processes

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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.
Original languageEnglish
Title of host publicationQuantitative Evaluation of Systems : 15th International Conference, QEST 2018, Beijing, China, September 4-7, 2018, Proceedings
EditorsAnabelle McIver, Andras Horvath
Number of pages17
Publication date4 Sep 2018
ISBN (Print)978-3-319-99153-5
ISBN (Electronic)978-3-319-99154-2
Publication statusPublished - 4 Sep 2018
EventQuantitative Evaluation of Systems 2018 - Beijing, China
Duration: 4 Sep 20187 Sep 2018


ConferenceQuantitative Evaluation of Systems 2018
Internet address
SeriesLecture Notes in Computer Science


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