Partial Conway and iteration semirings

Stephen L. Bloom, Zoltan Ésik, Werner Kuich

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

A Conway semiring is a semiring S equipped with a unary operation*: S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or Nrat≪Σ≫ of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conway identities. We introduce here partial Conway semirings, which are semirings S which have a star operation defined only on an ideal of S; when the arguments are appropriate, the operation satisfies the above identities. We develop the general theory of partial Conway semirings and prove a Kleene theorem for this generalization.

Original languageEnglish
Pages (from-to)19-40
Number of pages22
JournalFundamenta Informaticae
Volume86
Issue number1-2
Publication statusPublished - Nov 17 2008

Keywords

  • Conway semiring
  • Iteration semiring
  • Kleene theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Information Systems
  • Computational Theory and Mathematics

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    Bloom, S. L., Ésik, Z., & Kuich, W. (2008). Partial Conway and iteration semirings. Fundamenta Informaticae, 86(1-2), 19-40.