Model Checking Markov Chains Against Unambiguous Buchi Automata

An automaton is unambiguous if each word has at most one accepting run and separated if no word is accepted from two distinct states. The classical translation of LTL formulas to Büchi automata [5] produces unambiguous separated automata since the states of such automata correspond to complete subformula types. Motivated by this observation, Couvreur et al. [3] present a polynomialtime algorithm to model check Markov chains against separated unambiguous Büchi automata In this note we give a polynomial-time algorithm for model checking Markov chains against Büchi automata that are unambiguous but not necessarily separated. Apart from the extra generality of this procedure, our main motivation is the fact that the build-by-need translation from LTL to Büchi automata described in [1]—adapting the construction of [4]—produces automata that are unambiguous but which may not be separated.