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Quantum Finite One-Counter Automata

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Book cover SOFSEM’99: Theory and Practice of Informatics (SOFSEM 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1725))

Abstract

In this paper the notion of quantum finite one-counter automata (QF1CA) is introduced. Introduction of the notion is similar to that of the 2-way quantum finite state automata in [1]. The well-formedness conditions for the automata are specified ensuring unitarity of evolution. A special kind of QF1CA, called simple, that satisfies the well-formedness conditions is introduced. That allows specify rules for constructing such automata more naturally and simpler than in general case. Possible models of language recognition by QF1CA are considered. The recognition of some languages by QF1CA is shown and compared with recognition by probabilistic counterparts.

Supported by Grant No. 96.0282 from the Latvian Council of Science, Grant No. 1067 from the Sponsorship Programme of Latvian Fund of Education for Education, Science, and Culture.

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References

  1. Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In Proc. 38th FOCS (1997), 66–75.

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  2. Gruska, J.: Quantum Computing, McGraw Hill (1999).

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  3. Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In Proc. 39th FOCS (1998), 332–341.

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  4. Moore, C., Crutchfield, J. P.: Quantum Automata and Quantum Grammars http://xxx.lanl.gov/quant-ph/970731.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Latvia, Raina bulv. 19, Riga, Latvia

    Maksim Kravtsev

Authors
  1. Maksim Kravtsev
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Editor information

Editors and Affiliations

  1. DCIT, s.r.o, J. Martího 2/407, 162 02, Prague 6, Czech Republic

    Jan Pavelka

  2. Department of Computer Science, University of Utrecht, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Gerard Tel

  3. Institute of Computer Science, Masaryk University, Botanická 68a, 602 00, Brno, Czech Republic

    Miroslav Bartošek

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© 1999 Springer-Verlag Berlin Heidelberg

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Kravtsev, M. (1999). Quantum Finite One-Counter Automata. In: Pavelka, J., Tel, G., Bartošek, M. (eds) SOFSEM’99: Theory and Practice of Informatics. SOFSEM 1999. Lecture Notes in Computer Science, vol 1725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47849-3_31

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  • DOI: https://doi.org/10.1007/3-540-47849-3_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66694-3

  • Online ISBN: 978-3-540-47849-2

  • eBook Packages: Springer Book Archive

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