Probabilistic Büchi automata with non-extremal acceptance thresholds

Authors:
Rohit Chadha;A. Prasad Sistla;Mahesh Viswanathan
Affiliations:
LSV, ENS Cachan & CNRS & INRIA Saclay, France;Univ. of IIlinois, Chicago;Univ. of IIlinois, Urbana-Champaign
Venue:
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Year:
2011

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Abstract

This paper investigates the power of Probabilistic Büchi Automata (PBA) when the threshold probability of acceptance is non-extremal, i.e., is a value strictly between 0 and 1. Many practical randomized algorithms are designed to work under non-extremal threshold probabilities and thus it is important to study power of PBAs for such cases. The paper presents a number of surprising expressiveness and decidability results for PBAs when the threshold probability is non-extremal. Some of these results sharply contrast with the results for extremal threshold probabilities. The paper also presents results for Hierarchical PBAs and for an interesting subclass of them called simple PBAs.