On the Total Variation Distance of Semi-Markov Chains

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9 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 omega-languages recognized by timed automata. Computing this distance (i.e., solving its threshold problem) is NP-hard 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 : 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings
EditorsAndrew Pitts
Number of pages15
Volume9034
PublisherSpringer
Publication date2015
Pages185-199
ISBN (Print)978-3-662-46677-3
ISBN (Electronic)978-3-662-46678-0
DOIs
Publication statusPublished - 2015
Event18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, United Kingdom
Duration: 11 Apr 201518 Apr 2015
Conference number: 18

Conference

Conference18th International Conference on Foundations of Software Science and Computation Structures
Number18
LocationQueen Mary University
CountryUnited Kingdom
CityLondon
Period11/04/201518/04/2015
SeriesLecture Notes in Computer Science
ISSN0302-9743

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Markov processes
Computability and decidability
Model checking
Computational complexity
Specifications

Cite this

Bacci, G., Bacci, G., Larsen, K. G., & Mardare, R. I. (2015). On the Total Variation Distance of Semi-Markov Chains. In A. Pitts (Ed.), Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings (Vol. 9034, pp. 185-199). Springer. Lecture Notes in Computer Science https://doi.org/10.1007/978-3-662-46678-0_12
Bacci, Giorgio ; Bacci, Giovanni ; Larsen, Kim Guldstrand ; Mardare, Radu Iulian. / On the Total Variation Distance of Semi-Markov Chains. Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings. editor / Andrew Pitts. Vol. 9034 Springer, 2015. pp. 185-199 (Lecture Notes in Computer Science).
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Bacci, G, Bacci, G, Larsen, KG & Mardare, RI 2015, On the Total Variation Distance of Semi-Markov Chains. in A Pitts (ed.), Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings. vol. 9034, Springer, Lecture Notes in Computer Science, pp. 185-199, 18th International Conference on Foundations of Software Science and Computation Structures, London, United Kingdom, 11/04/2015. https://doi.org/10.1007/978-3-662-46678-0_12

On the Total Variation Distance of Semi-Markov Chains. / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand; Mardare, Radu Iulian.

Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings. ed. / Andrew Pitts. Vol. 9034 Springer, 2015. p. 185-199 (Lecture Notes in Computer Science).

Research output: Contribution to book/anthology/report/conference proceedingBook chapterResearchpeer-review

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AU - Mardare, Radu Iulian

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N2 - 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 omega-languages recognized by timed automata. Computing this distance (i.e., solving its threshold problem) is NP-hard and its decidability is an open problem. Nevertheless, we propose an algorithm for approximating it with arbitrary precision.

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Bacci G, Bacci G, Larsen KG, Mardare RI. On the Total Variation Distance of Semi-Markov Chains. In Pitts A, editor, Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings. Vol. 9034. Springer. 2015. p. 185-199. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-662-46678-0_12