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On the Size of One-way Quantum Finite Automata with Periodic Behaviors

We show that, for any stochastic event p of period n, there exists a measure-once one-way quantum finite automaton (1qfa) with at most 26n + 25 states inducing the event ap + b, for constants a > 0, b ≥ 0, satisfying a + b < 1. This fact is proved by designing an algorithm which constructs the desired lqfa in polynomial time. As a consequence, we get that any periodic language of period n can be accepted with isolated cut point by a lqfa with no more than 26n+26 states. Our results give added evidence of the strength of measure-once 1qfa's with respect to classical automata.