eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-24
22:1
22:15
10.4230/LIPIcs.CONCUR.2016.22
article
Computing Probabilistic Bisimilarity Distances via Policy Iteration
Tang, Qiyi
van Breugel, Franck
A transformation mapping a labelled Markov chain to a simple stochastic game is presented. In the resulting simple stochastic game, each vertex corresponds to a pair of states of the labelled Markov chain. The value of a vertex of the simple stochastic game is shown to be equal to the probabilistic bisimilarity distance, a notion due to Desharnais, Gupta, Jagadeesan and Panangaden, of the corresponding pair of states of the labelled Markov chain. Bacci, Bacci, Larsen and Mardare introduced an algorithm to compute the probabilistic bisimilarity distances for a labelled Markov chain. A modification of a basic version of their algorithm for a labelled Markov chain is shown to be the policy iteration algorithm applied to the corresponding simple stochastic game. Furthermore, it is shown that this algorithm takes exponential time in the worst case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol059-concur2016/LIPIcs.CONCUR.2016.22/LIPIcs.CONCUR.2016.22.pdf
labelled Markov chain
simple stochastic game
probabilistic bisimilarity
pseudometric
value function
policy iteration