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Equational Axioms for a Theory of Automata

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Formal Languages and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 148))

Summary

A Conway semiring is a starsemiring that satisfies the sum-star-equation and the product-star-equation. Many results in the theory of automata and languages only depend on the equations defining Conway semirings. We introduce semi-rings, formal power series and matrices, define Conway semirings and state some of their important properties. Then we prove a Kleene Theorem in Conway semirings. Eventually, we discuss the computation of the star of a matrix with entries in a Conway semiring.

Partially supported by Aktion Österreich-Ungarn, Wissenschafts und Erziehungskooperation, Projekt 53ÖU1.

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References

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Szeged, H-6701, Szeged, P.O.Box 652, Hungary

    Zoltán Ésik

  2. Institute für Algebra and Computermathematik, Technische Universität Wien, Wiedner Hptstr. 8-10, A-1040, Wien, Austria

    Werner Kuich

Authors
  1. Zoltán Ésik
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  2. Werner Kuich
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Lingustics, Rovira i Virgili University, Pl. Imperial Tàrraco 1, 43005, Tarragona, Spain

    Carlos Martín-Vide

  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania

    Victor Mitrana

  3. Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 2004 Springer-Verlag Berlin Heidelberg

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Ésik, Z., Kuich, W. (2004). Equational Axioms for a Theory of Automata. In: Martín-Vide, C., Mitrana, V., Păun, G. (eds) Formal Languages and Applications. Studies in Fuzziness and Soft Computing, vol 148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39886-8_10

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  • DOI: https://doi.org/10.1007/978-3-540-39886-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53554-3

  • Online ISBN: 978-3-540-39886-8

  • eBook Packages: Springer Book Archive

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