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 Buchi automata. We show that such automata are amenable to probabilistic model checking, similarly to unambiguous Buchi automata. We provide algorithms to translate $k$-ambiguous Buchi automata to image-binary Buchi automata, leading to model-checking algorithms with optimal computational complexity.
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