Algebraically complete semirings and Greibach normal form

Zoltán Ésik, Hans Leiß

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach's normal form theorem depends only on a few equational properties of least pre-fixed points in semirings, and eliminations of chain and deletion rules depend on their inequational properties (and the idempotence of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed points.

Original languageEnglish
Pages (from-to)173-203
Number of pages31
JournalAnnals of Pure and Applied Logic
Volume133
Issue number1-3 SPEC. ISS.
DOIs
Publication statusPublished - May 1 2005

Keywords

  • Algebraically complete semiring
  • Context-free languages
  • Conway semiring
  • Equational theory
  • Greibach normal form
  • Kleene algebra
  • Pre-fixed-point induction

ASJC Scopus subject areas

  • Logic

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