# Probabilistic Automata over Infinite Words: Expressiveness, Efficiency, and Decidability

@inproceedings{Baier2009ProbabilisticAO, title={Probabilistic Automata over Infinite Words: Expressiveness, Efficiency, and Decidability}, author={Christel Baier and Nathalie Bertrand and Marcus Gr{\"o}{\ss}er}, booktitle={DCFS}, year={2009} }

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…

## 9 Citations

### Max and Sum Semantics for Alternating Weighted Automata

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It is shown that universal weighted automata in the sum semantics can represent all polynomials, and it is argued that a summation semantics is of interest too, as it captures the intuition that one has to pay for the cost of all conjuncts.

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It follows from Krob's results that the universality problem is decidable for weighted automata with weights in N ∪ {∞}, and that the equality problem is undecidable when the weights are in N â‚¬∞.

### Use of Buchi automata and randomness for the description of biological processes

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Stochastic computational models with infinite input are used in this paper and indicative aspects of a biological problem are presented using both ω -automata and probabilistic Buchi automata, making a novel attempt to establish their use in reasoning about biological processes.

### Rigorous Approximated Determinization of Weighted Automata

- Computer Science2011 IEEE 26th Annual Symposium on Logic in Computer Science
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### Quantum ω-Automata over Infinite Words and Their Relationships

- Computer Science, PhysicsInternational Journal of Theoretical Physics
- 2019

This work has investigated the classes of quantum ω-automata from two aspects: the language recognition and their closure properties and shown that quantum Muller automaton is more dominant than quantum Büchi automaton.

### Language Equivalence for Probabilistic Automata

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A new randomised algorithm for deciding language equivalence for probabilistic automata based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small is proposed.

### Ambiguity, Weakness, and Regularity in Probabilistic Büchi Automata

- Computer ScienceFoSSaCS
- 2020

This work extends the known classes of restricted PBA which are still regular, and investigates the expressivity of the not yet considered but natural class of weak PBA, and shows that the regularity problem for strong PBA is undecidable.

### Algorithmic analysis of Regular repeated games

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Algorithmic Analysis of Regular Repeated Games shows clear trends in the number of games played and the quality of the games played increases with increasing number of rounds.

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