Probabilistic Automata over Infinite Words: Expressiveness, Efficiency, and Decidability
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2009
- DOI:
- 10.48550/arXiv.0907.4760
- arXiv:
- arXiv:0907.4760
- Bibcode:
- 2009arXiv0907.4760B
- Keywords:
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- Computer Science - Formal Languages and Automata Theory;
- F.4.3
- E-Print:
- EPTCS 3, 2009, pp. 3-16