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

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

12 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 language	English
Title of host publication	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
Editors	Andrew Pitts
Number of pages	15
Volume	9034
Publisher	Springer
Publication date	2015
Pages	185-199
ISBN (Print)	978-3-662-46677-3
ISBN (Electronic)	978-3-662-46678-0
DOIs	https://doi.org/10.1007/978-3-662-46678-0_12
Publication status	Published - 2015
Event	18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, United Kingdom Duration: 11 Apr 2015 → 18 Apr 2015 Conference number: 18

Conference

Conference	18th International Conference on Foundations of Software Science and Computation Structures
Number	18
Location	Queen Mary University
Country/Territory	United Kingdom
City	London
Period	11/04/2015 → 18/04/2015

Series	Lecture Notes in Computer Science
ISSN	0302-9743

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

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CASSTING: Collective Adaptive System SynThesIs using Non-zero-sum Games
Larsen, K. G., Skou, A., David, A. & Srba, J.
FP7 STREP
01/04/2013 → 31/03/2016
Project: Research
SENSATION: Self Energy-Supporting Autonomous Computation
Larsen, K. G., Hansen, R. R., Koch, P., Nielsen, B. & Skou, A.
FP7 FET Proactive
01/10/2012 → 30/09/2015
Project: Research
IDEA4CPS: Foundations for Cyber-Physical Sytems
Larsen, K. G., Skou, A., Nielsen, B., Bulychev, P., Ravn, A. P. & Poulsen, D. B.
01/04/2011 → 30/04/2015
Project: Research

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. 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. editor / Andrew Pitts. Vol. 9034 Springer, 2015. pp. 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}",

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language = "English",

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booktitle = "Foundations of Software Science and Computation Structures",

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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 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. ed. / Andrew Pitts. Vol. 9034 Springer, 2015. p. 185-199 (Lecture Notes in Computer Science).

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

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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.

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BT - Foundations of Software Science and Computation Structures

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

On the Total Variation Distance of Semi-Markov Chains

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Projects

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

SENSATION: Self Energy-Supporting Autonomous Computation

IDEA4CPS: Foundations for Cyber-Physical Sytems

Cite this