NDLI: Deciding the Value 1 Problem for Probabilistic Leaktight Automata

Content Provider	IEEE Xplore Digital Library
Author	Fijalkow, N. Gimbert, H. Oualhadj, Y.
Copyright Year	2012
Abstract	The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton, are there words accepted with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviors of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators.
Starting Page	295
Ending Page	304
File Size	271438
Page Count	10
File Format	PDF
ISBN	9781467322638
ISSN	10436871
DOI	10.1109/LICS.2012.40
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-25
Publisher Place	Croatia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automata Probabilistic logic Markov processes Transient analysis Electronic mail Process control Algebraic Techniques in Automata Theory Probabilistic automata Value 1 problem
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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