ملخص: Probabilistic ?-automata are variants of nondeterministic automata over infinite words where all choices are resolved by probabilistic distributions. Acceptance of a run for an infinite input word can be defined using traditional acceptance criteria for ?-automata, such as B¨ uchi, Rabin or Streett conditions. The accepted language of a probabilistic ?-automata is then defined by imposing a constraint on the probability measure of the accepting runs. In this paper, we study a series of fundamental properties of probabilistic ?-automata with three different language-semantics: (1) the probable semantics that requires positive acceptance probability,(2) the almost-sure semantics that requires acceptance with probability 1, and (3) the threshold semantics that relies on an additional parameter ? ?]0, 1[ that specifies a lower probability bound for the acceptance probability. We provide a comparison of probabilistic ?-automata under these three semantics and nondeterministic ?-automata concerning expressiveness and efficiency. Furthermore, we address closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment.

لغة: إنجليزية