Partial conway and iteration semiring-semimodule pairs

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

3 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 identities. A Conway semiring-semimodule pair consists of a Conway semiring S and a left S-semimodule V together with a function ω : S∈→∈V, called "omega power", subject to the sum omega and product omega identities. A Kleene type theorem holds in all Conway semiring-semimodule pairs that can be instantiated to give the equivalence of Büchi automata and regular languages over ω-words. However, sometimes the star and omega power operations cannot be defined in an appropriate manner on the whole semiring S. To handle this situation, we introduce partial Conway semiring-semimodule pairs and develop their basic theory in connection with automata. We prove a Kleene theorem, applicable to all partial Conway semiring-semimodule pairs.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages56-71
Number of pages16
Volume7020 LNCS
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7020 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Fingerprint

Semimodule
Semiring
Stars
Iteration
Partial
Star
Formal languages
Automata
Star Products
Regular Languages
Unary
Theorem
Equivalence

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ésik, Z. (2011). Partial conway and iteration semiring-semimodule pairs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7020 LNCS, pp. 56-71). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7020 LNCS). https://doi.org/10.1007/978-3-642-24897-9_3

Partial conway and iteration semiring-semimodule pairs. / Ésik, Z.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7020 LNCS 2011. p. 56-71 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7020 LNCS).

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

Ésik, Z 2011, Partial conway and iteration semiring-semimodule pairs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7020 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7020 LNCS, pp. 56-71. https://doi.org/10.1007/978-3-642-24897-9_3
Ésik Z. Partial conway and iteration semiring-semimodule pairs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7020 LNCS. 2011. p. 56-71. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-24897-9_3
Ésik, Z. / Partial conway and iteration semiring-semimodule pairs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7020 LNCS 2011. pp. 56-71 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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