Probabilistic $ømega$-Automata

Christel BaierChristel Baier, Nathalie BertrandNathalie Bertrand, Marcus GrößerMarcus Größer

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Christel Baier, Nathalie Bertrand, Marcus Größer
Probabilistic $ømega$-Automata
Journal of the ACM, 59(1), 2012

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KurzfassungAbstract
Probabilistic ω-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 ω-automata, such as Büchi, Rabin or Streett conditions. The accepted language of a probabilistic ω-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 ω-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 λ ∈ ]0,1[ that specifies a lower probability bound for the acceptance probability. We provide a comparison of probabilistic ω-automata under these three semantics and nondeterministic ω-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.
Forschungsgruppe:Research Group: Algebraische und logische Grundlagen der InformatikAlgebraic and Logical Foundations of Computer Science

@article{BBG2012,
  author  = {Christel Baier and Nathalie Bertrand and Marcus Gr{\"{o}}{\ss}er},
  title   = {Probabilistic ${\o}mega$-Automata},
  journal = {Journal of the {ACM}},
  volume  = {59},
  number  = {1},
  year    = {2012},
  doi     = {10.1145/2108242.2108243}
}