Author(s):

Chatterjee, Krishnendu; Tracol, Mathieu

Title: 
Decidable problems for probabilistic automata on infinite words

Affiliation 
IST Austria 
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 for every ε > 0 there is a word that is accepted with probability at least 1 − ε. 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 words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions.

Publication Title:

CoRR: Computing Research Repository

Volume: 
abs/1107.2091

Publisher:

ArXiv

Date Published:

20110411

URL: 

Open access: 
yes (repository) 