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Lower Bounds on the Size of Quantum Automata Accepting Unary Languages

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Theoretical Computer Science (ICTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2841))

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Abstract

In this paper, we study measure-once 1-way quantum automata accepting unary languages, i.e., of type L ⊂ {a}* . We give two lower bounds on the number of states of such automata accepting certain languages.

  1. 1

    We prove the existence of n-periodic languages requiring \(\Omega (\sqrt{\frac{n}{log n}})\) states to be recognized. This should be compared with results in the literature stating that every n-periodic language can be recognized with \(O(\sqrt{n})\) states.

  2. 2

    We give a lower bound on the number of states of automata accepting the finite language L < n = {a k ∈ L | k < n}, for a given L. This bound is obtained by using quantum information theory arguments.

Partially supported by MURST, under the project “Linguaggi formali: teoria ed applicazioni”.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, via Comelico 39/41, 20135, Milano, Italy

    Alberto Bertoni, Carlo Mereghetti & Beatrice Palano

Authors
  1. Alberto Bertoni
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  2. Carlo Mereghetti
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  3. Beatrice Palano
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Applicazioni, Università degli Studi di Salerno, Via Ponte Don Melillo, I-84084, Fisciano, SA, Italy

    Carlo Blundo

  2. Department of Computer Science, University of Bologna,  

    Cosimo Laneve

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Bertoni, A., Mereghetti, C., Palano, B. (2003). Lower Bounds on the Size of Quantum Automata Accepting Unary Languages. In: Blundo, C., Laneve, C. (eds) Theoretical Computer Science. ICTCS 2003. Lecture Notes in Computer Science, vol 2841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45208-9_8

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  • DOI: https://doi.org/10.1007/978-3-540-45208-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20216-5

  • Online ISBN: 978-3-540-45208-9

  • eBook Packages: Springer Book Archive

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