2008 | OriginalPaper | Chapter
Iteration Semirings
Author : Zoltán Ésik
Published in: Developments in Language Theory
Publisher: Springer Berlin Heidelberg
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A Conway semiring is a semiring
S
equipped with a unary operation
*
:
S
→
S
, 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.