Issue |
RAIRO-Theor. Inf. Appl.
Volume 36, Number 3, July/September 2002
|
|
---|---|---|
Page(s) | 277 - 291 | |
DOI | https://doi.org/10.1051/ita:2002014 | |
Published online | 15 December 2002 |
On the Size of One-way Quantum Finite Automata with Periodic Behaviors
1
Dipartimento di Informatica, Sist. e Com.,
Università degli Studi di Milano – Bicocca,
Via Bicocca degli Arcimboldi 8,
20126 Milano, Italy; mereghetti@disco.unimib.it.
2
Dipartimento di Informatica,
Università degli Studi di Torino,
Corso Svizzera 185,
10149 Torino, Italy; beatrice@di.unito.it.
Received:
19
February
2002
Accepted:
28
May
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.
Mathematics Subject Classification: 68Q10 / 68Q19 / 68Q45
Key words: Quantum finite automata / periodic events and languages
© EDP Sciences, 2002
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