Markov chains and unambiguous automata

Unambiguous automata are nondeterministic in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against ω-regular specifications represented as unambiguous automata. We furthermore show that the complexity of problem lies NC: subclass P comprising those problems solvable poly-logarithmic parallel time. These bounds match known given deterministic automata, notwithstanding fact can be exponentially more succinct than report on an implementation our procedure, including experiment is used to check LTL formulas chains.