  Probabilistic omega-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 omega-automata by means of a Buechi 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 omega-automata concerning
expressiveness, efficiency, and decision problems.
