We introduce a novel technique to analyse unambiguous Büchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant spectral radius. This method can replace a combinatorial procedure that dominates the computational complexity of the existing procedure by Baier et al. We analyse the complexity in detail, showing that, in terms of the set Q of states of the automaton, the new algorithm runs in time O(|Q| 4 ), improving on an efficient implementation of the combinatorial algorithm by a factor of |Q|.

We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for polynomial complementation, union, and intersection. This compares favourably with unambiguous automata whose complementation requires a superpolynomial state blowup. We also study an infinite-word version, image-binary Büchi automata. We show that such automata are amenable to probabilistic model checking, similarly to unambiguous Büchi automata. We provide algorithms to translate k-ambiguous Büchi automata to image-binary Büchi automata, leading to model-checking algorithms with optimal computational complexity.