Complete Axiomatization for the Bisimilarity Distance on Markov Chains

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2 Citationer (Scopus)

Resumé

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.
OriginalsprogEngelsk
Titel27th International Conference on Concurrency Theory (CONCUR 2016)
Antal sider14
ForlagSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH
Publikationsdato2016
Sider21:1--21:14
ISBN (Trykt)978-3-95977-017-0
DOI
StatusUdgivet - 2016
Begivenhed27th International Conference on Concurrency Theory - Université Laval, Québec City, Canada
Varighed: 23 aug. 201626 aug. 2016
Konferencens nummer: 27
http://www.concur2016.ulaval.ca/no_cache/home/

Konference

Konference27th International Conference on Concurrency Theory
Nummer27
LokationUniversité Laval
LandCanada
ByQuébec City
Periode23/08/201626/08/2016
Internetadresse
NavnLeibniz International Proceedings in Informatics
Vol/bind59
ISSN1868-8969

Fingerprint

Axiomatization
Markov chain
Equational Logic
Deductive System
Approximately equal
Axiom
Equality
Probability Distribution
Class
Style

Citer dette

Bacci, G., Bacci, G., Larsen, K. G., & Mardare, R. I. (2016). Complete Axiomatization for the Bisimilarity Distance on Markov Chains. I 27th International Conference on Concurrency Theory (CONCUR 2016) (s. 21:1--21:14). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH. Leibniz International Proceedings in Informatics, Bind. 59 https://doi.org/10.4230/LIPIcs.CONCUR.2016.21
Bacci, Giorgio ; Bacci, Giovanni ; Larsen, Kim Guldstrand ; Mardare, Radu Iulian. / Complete Axiomatization for the Bisimilarity Distance on Markov Chains. 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, 2016. s. 21:1--21:14 (Leibniz International Proceedings in Informatics, Bind 59).
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title = "Complete Axiomatization for the Bisimilarity Distance on Markov Chains",
abstract = "In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that {"}t is approximately equal to s up to an error e{"}. Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.",
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Bacci, G, Bacci, G, Larsen, KG & Mardare, RI 2016, Complete Axiomatization for the Bisimilarity Distance on Markov Chains. i 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Leibniz International Proceedings in Informatics, bind 59, s. 21:1--21:14, 27th International Conference on Concurrency Theory, Québec City, Canada, 23/08/2016. https://doi.org/10.4230/LIPIcs.CONCUR.2016.21

Complete Axiomatization for the Bisimilarity Distance on Markov Chains. / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand; Mardare, Radu Iulian.

27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, 2016. s. 21:1--21:14 (Leibniz International Proceedings in Informatics, Bind 59).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

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N2 - In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.

AB - In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.

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KW - Behavioral Distances

KW - Axiomatization

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SN - 978-3-95977-017-0

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Bacci G, Bacci G, Larsen KG, Mardare RI. Complete Axiomatization for the Bisimilarity Distance on Markov Chains. I 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH. 2016. s. 21:1--21:14. (Leibniz International Proceedings in Informatics, Bind 59). https://doi.org/10.4230/LIPIcs.CONCUR.2016.21