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Lower Bounds for Generalized Quantum Finite Automata

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Language and Automata Theory and Applications (LATA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5196))

Abstract

We obtain several lower bounds on the language recognition power of Nayak’s generalized quantum finite automata (GQFA) [12]. Techniques for proving lower bounds on Kondacs and Watrous’ one-way quantum finite automata (KWQFA) were introduced by Ambainis and Freivalds [2], and were expanded in a series of papers. We show that many of these techniques can be adapted to prove lower bounds for GQFAs. Our results imply that the class of languages recognized by GQFAs is not closed under union. Furthermore, we show that there are languages which can be recognized by GQFAs with probability p > 1/2, but not with p > 2/3.

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Author information

Authors and Affiliations

  1. Département d’Informatique, Université de Sherbrooke, QC, Canada

    Mark Mercer

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  1. Mark Mercer
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Plaza Imperial Tàrraco 1, 43005, Tarragona, Spain

    Carlos Martín-Vide

  2. Fachbereich Elektrotechnik/Informatik, Universität Kassel, Wilhelmshöher Allee 73, 34121, Kassel, Germany

    Friedrich Otto

  3. Fachbereich 4, Abteilung Informatik/Wirtschaftsinformatik, Universität Trier, Campus II, Gebäude H, 54286, Trier, Germany

    Henning Fernau

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Mercer, M. (2008). Lower Bounds for Generalized Quantum Finite Automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_34

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  • DOI: https://doi.org/10.1007/978-3-540-88282-4_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88281-7

  • Online ISBN: 978-3-540-88282-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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