Lower Bounds on the Size of Quantum Automata Accepting Unary Languages

  • Alberto Bertoni
  • Carlo Mereghetti
  • Beatrice Palano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)


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.



quantum automata quantum information theory 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alberto Bertoni
    • 1
  • Carlo Mereghetti
    • 1
  • Beatrice Palano
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly

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