A hemimetric extension of simulation for semi-markov decision processes

Mathias Ruggaard Pedersen, Giorgio Bacci, Kim Guldstrand Larsen, Radu Mardare

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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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, Proceedings
EditorsAnnabelle McIver, Andras Horvath
Place of PublicationCham
Number of pages17
ISBN (Print)9783319991535
Publication statusPublished - 4 Sep 2018
Event15th International Conference on Quantitative Evaluation of Systems, QEST 2018 - Beijing, China
Duration: 4 Sep 20187 Sep 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11024 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Conference on Quantitative Evaluation of Systems, QEST 2018


  • semi-Markov decision processes
  • Markovian logic


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