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Syntactic Semiring of a Language

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Mathematical Foundations of Computer Science 2001 (MFCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

A classical construction assigns to any language its (ordered) syntactic monoid. Recently the author defined the so-called syntactic semiring of a language. We discuss here the relationships between those two structures. Pin’s refinement of Eilenberg theorem gives a one-to-one correspondence between positive varieties of rational languages and pseudovarieties of ordered monoids. The author’s modification uses so-called conjunctive varieties of rational languages and pseudovarieties of idempotent semirings. We present here also several examples of our varieties of languages.

The author acknowledges the support of the Grant no. 201/01/0323 of the Grant Agency of the Czech Republic.

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References

  1. Almeida, J.; Finite Semigroups and Universal Algebra, World Scientific, 1994

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  2. Eilenberg, S.; Automata, Languages and Machines, Vol. B, Academic Press, 1976

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  3. Pin, J.-E.; Varieties of Formal Languages, Plenum, 1986

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  4. Pin, J.-E.; A variety theorem without complementation, Izvestiya VUZ Matematika 39 (1995) 80–90. English version: Russian Mathem. (Iz. VUZ) 39 (1995) 74-83

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  5. Pin, J.-E.; Syntactic semigroups, Chapter 10 in Handbook of Formal Languages, G. Rozenberg and A. Salomaa eds, Springer, 1997

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  6. Polák, L.; A classification of rational languages by semilattice-ordered monoids, http://www.math.muni.cz/~polak

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Author information

Authors and Affiliations

  1. Department of Mathematics, Masaryk University, Janáčkovo nám 2a, 662 95, Brno, Czech Republic

    Libor Polák

Authors
  1. Libor Polák
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Editor information

Editors and Affiliations

  1. Mathematical Institute, AS CR, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Sgall

  2. Faculty of Mathematics and Physics Institute for Theoretical Computer Science (ITI), Charles University, Malostranské náměstí 25, 118 00, Praha 1, Czech Republic

    Aleš Pultr  & Petr Kolman  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Polák, L. (2001). Syntactic Semiring of a Language. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_53

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  • DOI: https://doi.org/10.1007/3-540-44683-4_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

  • eBook Packages: Springer Book Archive

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