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Size Lower Bounds for Quantum Automata

  • Conference paper
Unconventional Computation and Natural Computation (UCNC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7956))

Abstract

We compare the descriptional power of quantum finite automata with control language (qfcs) and deterministic finite automata (dfas). By suitably adapting Rabin’s technique, we show how to convert any given qfc to an equivalent dfa, incurring in an at most exponential size increase. This enables us to state a lower bound on the size of qfcs, which is logarithmic in the size of equivalent minimal dfas. In turn, this result yields analogous size lower bounds for several models of quantum finite automata in the literature.

Partially supported by MIUR under the project “PRIN: Automi e Linguaggi Formali: Aspetti Matematici e Applicativi.”

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Authors and Affiliations

  1. Dip. Informatica, Univ. degli Studi di Milano, v. Comelico 39, 20135, Milano, Italy

    Maria Paola Bianchi, Carlo Mereghetti & Beatrice Palano

Authors
  1. Maria Paola Bianchi
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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, Sistemistica e Communicazione, UniversitĂ  degli Studi di Milano-Bicocca, Viale Sacra 336/14, 20126, Milan, Italy

    Giancarlo Mauri

  2. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano–Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Alberto Dennunzio  & Luca Manzoni  & 

  3. Dipartimento di Informatica, Sistemistica e Comunicazione, UniversitĂ  degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milano, Italy

    Antonio E. Porreca

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Bianchi, M.P., Mereghetti, C., Palano, B. (2013). Size Lower Bounds for Quantum Automata. In: Mauri, G., Dennunzio, A., Manzoni, L., Porreca, A.E. (eds) Unconventional Computation and Natural Computation. UCNC 2013. Lecture Notes in Computer Science, vol 7956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39074-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-39074-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39073-9

  • Online ISBN: 978-3-642-39074-6

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