On the total variation distance of semi-markov chains

Giorgio Bacci, Giovanni Bacci, Kim Guldstrand Larsen, Radu Mardare

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

10 Citations (Scopus)

Abstract

Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over linear real-time specifications. Specifically, we prove that the total variation between two SMCs coincides with the maximal difference w.r.t. the likelihood of satisfying arbitrary MTL formulas or ω-languages recognized by timed automata. Computing this distance (i.e., solving its threshold problem) is NPhard and its decidability is an open problem. Nevertheless, we propose an algorithm for approximating it with arbitrary precision.

Original languageEnglish
Title of host publicationFoundations of Software Science and Computation Structures
Subtitle of host publicationProceedings 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015
EditorsAndrew Pitts
Place of PublicationBerlin
PublisherSpringer-Verlag
Pages185-199
Number of pages15
Volume9034
ISBN (Print)9783662466773
DOIs
Publication statusPublished - 1 Jan 2015
Event18th International Conference on Foundations of Software Science and Computation Structures, FoSSaCS 2015 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015 - London, United Kingdom
Duration: 11 Apr 201518 Apr 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9034
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference on Foundations of Software Science and Computation Structures, FoSSaCS 2015 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015
CountryUnited Kingdom
CityLondon
Period11/04/1518/04/15

Keywords

  • model check
  • measurable space
  • coupling structure
  • arbitrary precision
  • total variation distance

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  • Cite this

    Bacci, G., Bacci, G., Larsen, K. G., & Mardare, R. (2015). On the total variation distance of semi-markov chains. In A. Pitts (Ed.), Foundations of Software Science and Computation Structures: Proceedings 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015 (Vol. 9034, pp. 185-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9034). Berlin: Springer-Verlag. https://doi.org/10.1007/978-3-662-46678-0_12