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

Carlo Mereghetti; Beatrice Palano

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 3, page 277-291
  • ISSN: 0988-3754

Abstract

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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 6 n + 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 6 n + 26 states. Our results give added evidence of the strength of measure-once 1qfa's with respect to classical automata.

How to cite

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Mereghetti, Carlo, and Palano, Beatrice. "On the Size of One-way Quantum Finite Automata with Periodic Behaviors." RAIRO - Theoretical Informatics and Applications 36.3 (2010): 277-291. <http://eudml.org/doc/92702>.

@article{Mereghetti2010,
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. },
author = {Mereghetti, Carlo, Palano, Beatrice},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Quantum finite automata; periodic events and languages; measure-once one-way quantum finite automaton},
language = {eng},
month = {3},
number = {3},
pages = {277-291},
publisher = {EDP Sciences},
title = {On the Size of One-way Quantum Finite Automata with Periodic Behaviors},
url = {http://eudml.org/doc/92702},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Mereghetti, Carlo
AU - Palano, Beatrice
TI - On the Size of One-way Quantum Finite Automata with Periodic Behaviors
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 3
SP - 277
EP - 291
AB - 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.
LA - eng
KW - Quantum finite automata; periodic events and languages; measure-once one-way quantum finite automaton
UR - http://eudml.org/doc/92702
ER -

References

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