A Class of Probabilistic Automata with a Decidable Value 1 Problem

The value 1 problem is a decision problem for probabilistic automata on finite words: given a probabilistic automaton A, are there words accepted by A 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. rithm is based on the computation of a monoid abstracting the behaviors of the automaton. The correctness proof relies on algebraic techniques developed by Simon.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Nathanaël Fijalkow, Hugo Gimbert, Youssouf Oualhadj
• Keywords: CORR 2011, Decision Problem, Education, Probabilistic Automata, Probabilistic Automaton