Probabilistic Automata over Infinite Words: Expressiveness, Efficiency, and Decidability
Abstract
Probabilistic omegaautomata 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 (almostsure 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 omegaautomata 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 omegaautomata concerning expressiveness, efficiency, and decision problems.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 DOI:
 10.48550/arXiv.0907.4760
 arXiv:
 arXiv:0907.4760
 Bibcode:
 2009arXiv0907.4760B
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 F.4.3
 EPrint:
 EPTCS 3, 2009, pp. 316