On the size of one-way quantum finite automata with periodic behaviors

Mereghetti, Carlo; Palano, Beatrice

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 3, pp. 277-291.

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 $2\sqrt{6n}+25$ states inducing the event $ap+b$, for constants $a>0$, $b\ge 0$, satisfying $a+b\le 1$. 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 $2\sqrt{6n}+26$ states. Our results give added evidence of the strength of measure-once 1qfa’s with respect to classical automata.

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