Greibach normal form in algebraically complete semirings

Zoltán Ésik, Hans Leiß

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 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 elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points.

Original languageEnglish
Title of host publicationComputer Science Logic - 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL 2002, Proceedings
EditorsJulian Bradfield
PublisherSpringer Verlag
Pages135-150
Number of pages16
ISBN (Print)3540442405, 9783540442400
Publication statusPublished - Jan 1 2002
Event16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002 - Edinburgh, United Kingdom
Duration: Sep 22 2002Sep 25 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2471
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002
CountryUnited Kingdom
CityEdinburgh
Period9/22/029/25/02

    Fingerprint

Keywords

  • Algebraically complete semirings
  • Context-free languages
  • Conway algebra
  • Equational theory
  • Greibach normal form
  • Kleene algebra
  • Pre-fixedpoint induction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ésik, Z., & Leiß, H. (2002). Greibach normal form in algebraically complete semirings. In J. Bradfield (Ed.), Computer Science Logic - 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL 2002, Proceedings (pp. 135-150). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2471). Springer Verlag.