Revisiting the Power and Equivalence of One-Way Quantum Finite Automata

We give a new proof for the fact that measure-many one-way quantum finite automata (MM-1QFA) recognize only regular languages with bounded error. Our proof, different from the one in the literature, gives another insight to the recognition power of MM-1QFA. Moreover, we generalize the proof to a broader class of automata that include probabilistic automata and some kinds of quantum finite automata. In addition, we briefly discuss the equivalence problem of some quantum computing models in a uniform framework.

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