A Class of Probabilistic Automata with a Decidable Value 1 Problem

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 introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is decidable. The algorithm is based on the computation of a monoid abstracting the behaviors of the automaton. The correctness proof relies on algebraic techniques developped by Simon.

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