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

Published online by Cambridge University Press:  15 December 2002

Carlo Mereghetti  and
Beatrice Palano
Carlo Mereghetti
Affiliation:
Dipartimento di Informatica, Sist. e Com., Università degli Studi di Milano – Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy; mereghetti@disco.unimib.it.
Beatrice Palano
Affiliation:
Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, 10149 Torino, Italy; beatrice@di.unito.it.
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Abstract

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 ≥ 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 $2\sqrt{6n}+26$ states. Our results give added evidence of the strength of measure-once 1qfa's with respect to classical automata.

Keywords

Quantum finite automataperiodic events and languages
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 3 , July 2002 , pp. 277 - 291
Copyright
© EDP Sciences, 2002

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