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Upper Bounds on the Size of One-Way Quantum Finite Automata

  • Carlo Mereghetti
  • Beatrice Palano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2202)

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 automata periodic events and languages 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Carlo Mereghetti
    • 1
  • Beatrice Palano
    • 2
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano - BicoccaMilanoItaly
  2. 2.Dipartimento di InformaticaUniversità degli Studi di TorinoTorinoItaly

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