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International Conference on Unconventional Computation

UC 2010: Unconventional Computation pp 188Cite as

Quantum Finite State Automata over Infinite Words

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6079))

Abstract

The study of finite state automata working on infinite words was initiated by Büchi [1]. Büchi discovered connection between formulas of the monadic second order logic of infinite sequences (S1S) and ω-regular languages, the class of languages over infinite words accepted by finite state automata. Few years later, Muller proposed an alternative definition of finite automata on infinite words [4]. McNaughton proved that with Muller’s definition, deterministic automata recognize all ω-regular languages [2]. Later, Rabin extended decidability result of Büchi for S1S to the monadic second order of the infinite binary tree (S2S) [5]. Rabin theorem can be used to settle a number of decision problems in logic. A theory of automata over infinite words has started from these studies.

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References

  1. Büchi, J.R.: On a decision method in restricted second order arithmetic. Z. Math. Logik Grundlag. Math. 6, 66–92 (1960)

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  2. McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Inform. Control 9, 521–530 (1966)

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  3. Moore, C., Crutchfield, J.: Quantum automata and quantum grammars Theoretical Computer Science 237, 275–306 (2000)

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  4. Muller, D.E.: Infinite sequences an finite machines. In: Proc. 4th IEEE Symp. on Switching Circuit Theory and Logical Design, pp. 3–16 (1963)

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  5. Rabin, M.O.: Decidability of second order theories and automata on infinite trees. Trans. AMS 141, 1–37 (1969)

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raina 29, Riga, LV-1459, Latvia

    Ilze Dzelme-Bērziņa

Authors
  1. Ilze Dzelme-Bērziņa
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Auckland, Science Centre, 38 Princes Street, 1142, Auckland, New Zealand

    Cristian S. Calude

  2. Graduate School of Information Science and Technology, Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Masami Hagiya

  3. Graduate School of Engineering, Department of Information Engineering, Hiroshima University, 739-8527, Higashi-Hiroshima, Japan

    Kenichi Morita

  4. Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  5. Department of Computer Science and Department of Electronics, University of York, YO10 5DD, Heslington, York, UK

    Jon Timmis

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Dzelme-Bērziņa, I. (2010). Quantum Finite State Automata over Infinite Words. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds) Unconventional Computation. UC 2010. Lecture Notes in Computer Science, vol 6079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13523-1_21

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  • DOI: https://doi.org/10.1007/978-3-642-13523-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13522-4

  • Online ISBN: 978-3-642-13523-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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