On the Total Variation Distance of Semi-Markov Chains

Giorgio Bacci; Giovanni Bacci; Kim Guldstrand Larsen; Radu Iulian Mardare

doi:10.1007/978-3-662-46678-0_12

On the Total Variation Distance of Semi-Markov Chains

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

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Bidrag til bog/antologi › Forskning › peer review

12 Citationer (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.

Originalsprog	Engelsk
Titel	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
Redaktører	Andrew Pitts
Antal sider	15
Vol/bind	9034
Forlag	Springer
Publikationsdato	2015
Sider	185-199
ISBN (Trykt)	978-3-662-46677-3
ISBN (Elektronisk)	978-3-662-46678-0
DOI	https://doi.org/10.1007/978-3-662-46678-0_12
Status	Udgivet - 2015
Begivenhed	18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, Storbritannien Varighed: 11 apr. 2015 → 18 apr. 2015 Konferencens nummer: 18

Konference

Konference	18th International Conference on Foundations of Software Science and Computation Structures
Nummer	18
Lokation	Queen Mary University
Land/Område	Storbritannien
By	London
Periode	11/04/2015 → 18/04/2015

Navn	Lecture Notes in Computer Science
ISSN	0302-9743

Adgang til dokumentet

10.1007/978-3-662-46678-0_12

AUB Link

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Citationsformater

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. https://doi.org/10.1007/978-3-662-46678-0_12

Bacci, Giorgio ; Bacci, Giovanni ; Larsen, Kim Guldstrand et al. / 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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title = "On the Total Variation Distance of Semi-Markov Chains",

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}",

year = "2015",

doi = "10.1007/978-3-662-46678-0_12",

language = "English",

isbn = "978-3-662-46677-3",

volume = "9034",

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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, 18th International Conference on Foundations of Software Science and Computation Structures, 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 et al.
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 proceeding › Bidrag til bog/antologi › Forskning › peer review

TY - CHAP

T1 - On the Total Variation Distance of Semi-Markov Chains

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AU - Bacci, Giovanni

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu Iulian

N1 - Conference code: 18

PY - 2015

Y1 - 2015

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.

AB - 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.

U2 - 10.1007/978-3-662-46678-0_12

DO - 10.1007/978-3-662-46678-0_12

M3 - Book chapter

SN - 978-3-662-46677-3

VL - 9034

T3 - Lecture Notes in Computer Science

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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). doi: 10.1007/978-3-662-46678-0_12

On the Total Variation Distance of Semi-Markov Chains

Abstract

Konference

Adgang til dokumentet

AUB Link

Fingeraftryk

Projekter

CASSTING: Collective Adaptive System SynThesIs using Non-zero-sum Games

SENSATION: Self Energy-Supporting Autonomous Computation

IDEA4CPS: Foundations for Cyber-Physical Sytems

Citationsformater