文章基本信息

标题：Recurrence and Transience for Probabilistic Automata
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作者：Mathieu Tracol ; Christel Baier ; Marcus Gr{\"o}sser 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：4
页码：395-406
DOI：10.4230/LIPIcs.FSTTCS.2009.2335
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In a context of $\omega$-regular specifications for infinite execution sequences, the classical B\"uchi condition, or repeated liveness condition, asks that an accepting state is visited infinitely often. In this paper, we show that in a probabilistic context it is relevant to strengthen this infinitely often condition. An execution path is now accepting if the \emph{proportion} of time spent on an accepting state does not go to zero as the length of the path goes to infinity. We introduce associated notions of recurrence and transience for non-homogeneous finite Markov chains and study the computational complexity of the associated problems. As Probabilistic B\"uchi Automata (PBA) have been an attempt to generalize B\"uchi automata to a probabilistic context, we define a class of Constrained Probabilistic Automata with our new accepting condition on runs. The accepted language is defined by the requirement that the measure of the set of accepting runs is positive (probable semantics) or equals 1 (almost-sure semantics). In contrast to the PBA case, we prove that the emptiness problem for the language of a constrained probabilistic B\"uchi automaton with the probable semantics is decidable.
关键词：Markov Chains; Probabilistic Automata; Buchi Automata; Recurrence; Omega-Regular Properties