10.1109/LICS.2012.29
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Tracol, Mathieu
Mathieu
Tracol
Decidable problems for probabilistic automata on infinite words
IEEE
2012
2018-12-11T12:00:33Z
2020-01-21T13:20:00Z
conference
https://research-explorer.app.ist.ac.at/record/2957
https://research-explorer.app.ist.ac.at/record/2957.json
1107.2091
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.