Iteration semirings

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

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages1-20
Number of pages20
Volume5257 LNCS
DOIs
Publication statusPublished - 2008
Event12th International Conference on Developments in Language Theory, DLT 2008 - Kyoto, Japan
Duration: Sep 16 2008Sep 19 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5257 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th International Conference on Developments in Language Theory, DLT 2008
CountryJapan
CityKyoto
Period9/16/089/19/08

Fingerprint

Semiring
Stars
Iteration
Formal languages
Axiomatization
Star
Star Products
Equational Theory
Regular Languages
Unary
Power series

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ésik, Z. (2008). Iteration semirings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5257 LNCS, pp. 1-20). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5257 LNCS). https://doi.org/10.1007/978-3-540-85780-8_1

Iteration semirings. / Ésik, Z.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5257 LNCS 2008. p. 1-20 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5257 LNCS).

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

Ésik, Z 2008, Iteration semirings. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5257 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5257 LNCS, pp. 1-20, 12th International Conference on Developments in Language Theory, DLT 2008, Kyoto, Japan, 9/16/08. https://doi.org/10.1007/978-3-540-85780-8_1
Ésik Z. Iteration semirings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5257 LNCS. 2008. p. 1-20. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-85780-8_1
Ésik, Z. / Iteration semirings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5257 LNCS 2008. pp. 1-20 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{f376780b73444347ba099e84c51d287a,
title = "Iteration semirings",
abstract = "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.",
author = "Z. {\'E}sik",
year = "2008",
doi = "10.1007/978-3-540-85780-8_1",
language = "English",
isbn = "3540857796",
volume = "5257 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "1--20",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Iteration semirings

AU - Ésik, Z.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=54249163721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54249163721&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85780-8_1

DO - 10.1007/978-3-540-85780-8_1

M3 - Conference contribution

AN - SCOPUS:54249163721

SN - 3540857796

SN - 9783540857792

VL - 5257 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 20

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -