On the Size of One-way Quantum Finite Automata with Periodic Behaviors
Carlo Mereghetti, Beatrice Palano · RAIRO - Theoretical Informatics and Applications · 2002
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 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 1qfa in polynomial time. As a consequence, we get that any periodic language of period n can be accepted with isolated cut point by a 1qfa with no more than states. Our results give added evidence of the strength of measure-once 1qfa's with respect to classical automata.