Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

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Resumé

The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games. The correctness of Condon's approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP cap coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to Mémoli plays a central rôle.
OriginalsprogEngelsk
TidsskriftLeibniz International Proceedings in Informatics
Vol/bind140
Sider (fra-til)1
Antal sider17
ISSN1868-8969
DOI
StatusUdgivet - 2019
Begivenhed30th International Conference on Concurrency Theory - Amsterdam, Holland
Varighed: 26 aug. 201931 aug. 2019
Konferencens nummer: 30
https://event.cwi.nl/concur2019/

Konference

Konference30th International Conference on Concurrency Theory
Nummer30
LandHolland
ByAmsterdam
Periode26/08/201931/08/2019
Internetadresse

Citer dette

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title = "Computing Probabilistic Bisimilarity Distances for Probabilistic Automata",
abstract = "The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games. The correctness of Condon's approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP cap coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to M{\'e}moli plays a central r{\^o}le.",
author = "Giorgio Bacci and Giovanni Bacci and Larsen, {Kim Guldstrand} and Radu Mardare and Qiyi Tang and {van Breugel}, Franck",
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journal = "Leibniz International Proceedings in Informatics",
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Computing Probabilistic Bisimilarity Distances for Probabilistic Automata. / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand; Mardare, Radu; Tang, Qiyi; van Breugel, Franck.

I: Leibniz International Proceedings in Informatics, Bind 140, 2019, s. 1.

Publikation: Bidrag til tidsskriftKonferenceartikel i tidsskriftForskningpeer review

TY - GEN

T1 - Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

AU - Bacci, Giorgio

AU - Bacci, Giovanni

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu

AU - Tang, Qiyi

AU - van Breugel, Franck

PY - 2019

Y1 - 2019

N2 - The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games. The correctness of Condon's approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP cap coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to Mémoli plays a central rôle.

AB - The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games. The correctness of Condon's approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP cap coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to Mémoli plays a central rôle.

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JO - Leibniz International Proceedings in Informatics

JF - Leibniz International Proceedings in Informatics

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