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Integer Weighted Finite Automata, Matrices, and Formal Power Series over Laurent Polynomials

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Theory Is Forever

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3113))

Abstract

It is well known that the family of regular languages (over alphabet A), accepted by finite automata, coincides with the set of supports of the rational and recognizable formal power series over ℕ with the set of variables A. Here we prove that there is a corresponding presentation for languages accepted by integer weighted finite automata, where the weights are from the additive group of integers, via the matrices over Laurent polynomials with integer coefficients.

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Author information

Authors and Affiliations

  1. Department of Mathematics and TUCS – Turku Centre for Computer Science, University of Turku, FIN-20014, Turku, Finland

    Vesa Halava

Authors
  1. Vesa Halava
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  2. Institute for Information Systems and Computer Media (IICM), Graz University of Technology, A-8010, Graz, Austria

    Hermann Maurer

  3. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

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

    Grzegorz Rozenberg

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© 2004 Springer-Verlag Berlin Heidelberg

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Halava, V. (2004). Integer Weighted Finite Automata, Matrices, and Formal Power Series over Laurent Polynomials. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_8

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  • DOI: https://doi.org/10.1007/978-3-540-27812-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22393-1

  • Online ISBN: 978-3-540-27812-2

  • eBook Packages: Springer Book Archive

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