Probabilistic Automata over InfiniteWords: Expressiveness, Efficiency, and Decidability∗

Probabilistic w-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring that (i) the probability for the accepting runs is positive (probable semantics), or (ii) almost all runs are accepting (almost-sure semantics), or (iii) the probability measure of the accepting runs is greater than a certain threshold (threshold semantics). The underlying notion of an accepting run can be defined as for standard w-automata by means of a Biichi condition or other acceptance conditions, e. g., Rabin or Streett conditions. In this paper, we put the main focus on the probable semantics and provide a summary of the fundamental properties of probabilistic w-automata concerning expressiveness, efficiency, and decision problems.