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One-Way Finite Automata with Quantum and Classical States

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Languages Alive

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7300))

Abstract

In this paper, we introduce and explore a new model of quantum finite automata (QFA). Namely, one-way finite automata with quantum and classical states (1QCFA), a one way version of two-way finite automata with quantum and classical states (2QCFA) introduced by Ambainis and Watrous in 2002 [3]. First, we prove that coin-tossing one-way probabilistic finite automata (coin-tossing 1PFA) [23] and one-way quantum finite automata with control language (1QFACL) [6] as well as several other models of QFA, can be simulated by 1QCFA. Afterwards, we explore several closure properties for the family of languages accepted by 1QCFA. Finally, the state complexity of 1QCFA is explored and the main succinctness result is derived. Namely, for any prime m and any ε1 > 0, there exists a language L m that cannot be recognized by any measure-many one-way quantum finite automata (MM-1QFA) [12] with bounded error \(\frac{7}{9}+\epsilon_1\), and any 1PFA recognizing it has at last m states, but L m can be recognized by a 1QCFA for any error bound ε > 0 with O(logm) quantum states and 12 classical states.

This work is supported in part by the National Natural Science Foundation of China (Nos. 60873055, 61073054,61100001), the Natural Science Foundation of Guangdong Province of China (No. 10251027501000004), the Fundamental Research Funds for the Central Universities (Nos. 10lgzd12,11lgpy36), the Research Foundation for the Doctoral Program of Higher School of Ministry of Education (Nos. 20100171110042, 20100171120051) of China, the Czech Ministry of Education (No. MSM0021622419), the China Postdoctoral Science Foundation project (Nos. 20090460808, 201003375), and the project of SQIG at IT, funded by FCT and EU FEDER projects projects QSec PTDC/EIA/67661/2006, AMDSC UTAustin/MAT/0057/2008, NoE Euro-NF, and IT Project QuantTel, FCT project PTDC/EEA-TEL/103402/2008 QuantPrivTel.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Shenggen Zheng, Daowen Qiu & Lvzhou Li

  2. Faculty of Informatics, Masaryk University, Brno, 602 00, Czech Republic

    Jozef Gruska

  3. SQIG–Instituto de Telecomunicações, Departamento de Matemática, Instituto Superior Técnico, TULisbon, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Daowen Qiu

  4. The State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Daowen Qiu

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  1. Shenggen Zheng
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  2. Daowen Qiu
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  3. Lvzhou Li
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  4. Jozef Gruska
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Editors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  3. Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39016, Magdeburg, Germany

    Bianca Truthe

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Zheng, S., Qiu, D., Li, L., Gruska, J. (2012). One-Way Finite Automata with Quantum and Classical States. In: Bordihn, H., Kutrib, M., Truthe, B. (eds) Languages Alive. Lecture Notes in Computer Science, vol 7300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31644-9_19

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  • DOI: https://doi.org/10.1007/978-3-642-31644-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31643-2

  • Online ISBN: 978-3-642-31644-9

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