On the Total Variation Distance of Semi-Markov Chains

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9 Citationer (Scopus)

Resumé

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.
OriginalsprogEngelsk
TitelFoundations 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
RedaktørerAndrew Pitts
Antal sider15
Vol/bind9034
ForlagSpringer
Publikationsdato2015
Sider185-199
ISBN (Trykt)978-3-662-46677-3
ISBN (Elektronisk)978-3-662-46678-0
DOI
StatusUdgivet - 2015
Begivenhed18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, Storbritannien
Varighed: 11 apr. 201518 apr. 2015
Konferencens nummer: 18

Konference

Konference18th International Conference on Foundations of Software Science and Computation Structures
Nummer18
LokationQueen Mary University
LandStorbritannien
ByLondon
Periode11/04/201518/04/2015
NavnLecture Notes in Computer Science
ISSN0302-9743

Fingerprint

Markov processes
Computability and decidability
Model checking
Computational complexity
Specifications

Citer dette

Bacci, G., Bacci, G., Larsen, K. G., & Mardare, R. I. (2015). On the Total Variation Distance of Semi-Markov Chains. I A. Pitts (red.), 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 (Bind 9034, s. 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. red. / Andrew Pitts. Bind 9034 Springer, 2015. s. 185-199 (Lecture Notes in Computer Science).
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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.",
author = "Giorgio Bacci and Giovanni Bacci and Larsen, {Kim Guldstrand} and Mardare, {Radu Iulian}",
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Bacci, G, Bacci, G, Larsen, KG & Mardare, RI 2015, On the Total Variation Distance of Semi-Markov Chains. i A Pitts (red.), 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. bind 9034, Springer, Lecture Notes in Computer Science, s. 185-199, London, Storbritannien, 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. red. / Andrew Pitts. Bind 9034 Springer, 2015. s. 185-199 (Lecture Notes in Computer Science).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingBidrag til bog/antologiForskningpeer review

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Bacci G, Bacci G, Larsen KG, Mardare RI. On the Total Variation Distance of Semi-Markov Chains. I Pitts A, red., 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. Bind 9034. Springer. 2015. s. 185-199. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-662-46678-0_12