A Conway semiring is a semiring S equipped with a unary operation *:SS, called star, satisfying the sum star and product star equations. An iteration semiring is a Conway semiring satisfying Conway’s group equations. In this extended abstract, we review the role of iteration semirings in the axiomatization of regular languages and rational power series, and in the axiomatization of the equational theory of continuous and complete semirings.


Equational Theory Regular Language Functional Matrice Ideal Term Star Equation 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zoltán Ésik
    • 1
  1. 1.Research Group on Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain

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