# Decidable problems for probabilistic automata on infinite words

K. Chatterjee, M. Tracol, in:, Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012.

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Abstract

We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether words are accepted with probability arbitrarily close to 1. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape (regular) words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions. For most decidable problems we show an optimal PSPACE-complete complexity bound.

Publishing Year

Date Published

2012-08-23

Proceedings Title

Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science

Article Number

6280437

Conference

LICS: Logic in Computer Science

Conference Location

Dubrovnik, Croatia

Conference Date

2012-06-25 – 2012-06-28

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### Cite this

Chatterjee K, Tracol M. Decidable problems for probabilistic automata on infinite words. In:

*Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science*. IEEE; 2012. doi:10.1109/LICS.2012.29Chatterjee, K., & Tracol, M. (2012). Decidable problems for probabilistic automata on infinite words. In

*Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science*. Dubrovnik, Croatia : IEEE. https://doi.org/10.1109/LICS.2012.29Chatterjee, Krishnendu, and Mathieu Tracol. “Decidable Problems for Probabilistic Automata on Infinite Words.” In

*Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science*. IEEE, 2012. https://doi.org/10.1109/LICS.2012.29.K. Chatterjee and M. Tracol, “Decidable problems for probabilistic automata on infinite words,” in

*Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science*, Dubrovnik, Croatia , 2012.Chatterjee K, Tracol M. 2012. Decidable problems for probabilistic automata on infinite words. Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science

Chatterjee, Krishnendu, and Mathieu Tracol. “Decidable Problems for Probabilistic Automata on Infinite Words.”

*Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science*, 6280437, IEEE, 2012, doi:10.1109/LICS.2012.29.### Export

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arXiv 1107.2091