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 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 PSPACEcomplete complexity bound.

Keywords: 
almost and limit decision problems; Automata and formal languages; Parity conditions; Positive; Probabilistic automata

Conference Title:

LICS: Logic in Computer Science

Conference Dates:

June 25  28, 2012

Conference Location:

Dubrovnik, Croatia

ISBN:

9781479988754

Publisher:

IEEE

Date Published:

20120101

Start Page: 
185

End Page:

194

URL: 

DOI: 
10.1109/LICS.2012.29

Open access: 
yes (repository) 