eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-31
9:1
9:17
10.4230/LIPIcs.CONCUR.2018.9
article
Deciding Probabilistic Bisimilarity Distance One for Probabilistic Automata
Tang, Qiyi
1
van Breugel, Franck
2
Department of Computing, Imperial College, London, United Kingdom
Department of Electrical Engineering and Computer Science, York University, Toronto, Canada
Probabilistic bisimilarity, due to Segala and Lynch, is an equivalence relation that captures which states of a probabilistic automaton behave exactly the same. Deng, Chothia, Palamidessi and Pang proposed a robust quantitative generalization of probabilistic bisimilarity. Their probabilistic bisimilarity distances of states of a probabilistic automaton capture the similarity of their behaviour. The smaller the distance, the more alike the states behave. In particular, states are probabilistic bisimilar if and only if their distance is zero.
Although the complexity of computing probabilistic bisimilarity distances for probabilistic automata has already been studied and shown to be in NP cap coNP and PPAD, we are not aware of any practical algorithm to compute those distances. In this paper we provide several key results towards algorithms to compute probabilistic bisimilarity distances for probabilistic automata. In particular, we present a polynomial time algorithm that decides distance one. Furthermore, we give an alternative characterization of the probabilistic bisimilarity distances as a basis for a policy iteration algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol118-concur2018/LIPIcs.CONCUR.2018.9/LIPIcs.CONCUR.2018.9.pdf
probabilistic automaton
probabilistic bisimilarity
distance