Quantum Finite Automata with One-Sided Unbounded Error

We prove that several variants of the quantum finite automaton (QFA) model are strictly superior to their probabilistic counterparts, in terms of both language recognition power and succinctness, in the one-sided unbounded error setting. This is the first case where one-way QFA models have been shown to outperform the corresponding probabilistic automata in both these respects. We give a characterization of the class of languages recognized by these QFA's with cutpoint 0, demonstrating that it is equal to the class of exclusive stochastic languages. We prove several closure properties of the related classes.