Quantum finite automata using ancilla qubits
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We introduce a new model of quantum finite automata. By using
ancilla qubits, it becomes possible to recognize any regular
language with certainty. Some nonregular languages can be
recognized with one-sided unbounded error. We analyze a class
of languages that can be recognized in this model in terms of
a cascade composition of automata. This also allows to treat
the case of an automaton with both classical and quantum states.