Continuous semiring-semimodule pairs and mixed algebraic systems

Z. Ésik, Werner Kuich

Research output: Contribution to journalArticle

Abstract

We associate with every commutative continuous semiring S and alphabet S a category whose objects are all sets and a morphism X → Y is determined by a function from X into the semiring of formal series St(Y ∪+ ∗).y of finite words over Y ∪+, an X × Y -matrix over St(Y ∪+∗).y, and a function from X into the continuous St(Y ∪+∗).y-semimodule St(Y ∪+)ωy of series of ω- words over Y ∪+. When S is also an ω-semiring (equipped with an infinite product operation), then we define a fixed point operation over our category and show that it satisfies all identities of iteration categories. We then use this fixed point operation to give semantics to recursion schemes defining series of finite and infinite words. In the particular case when the semiring is the Boolean semiring, we obtain the context-free languages of finite and !-words.

Original languageEnglish
Pages (from-to)61-79
Number of pages19
JournalActa Cybernetica
Volume23
Issue number1
DOIs
Publication statusPublished - Jan 1 2017

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Semimodule
Semiring
Context free languages
Semantics
Series
Fixed point
Infinite Words
Context-free Languages
Infinite product
Morphism
Recursion
Iteration

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Continuous semiring-semimodule pairs and mixed algebraic systems. / Ésik, Z.; Kuich, Werner.

In: Acta Cybernetica, Vol. 23, No. 1, 01.01.2017, p. 61-79.

Research output: Contribution to journalArticle

Ésik, Z. ; Kuich, Werner. / Continuous semiring-semimodule pairs and mixed algebraic systems. In: Acta Cybernetica. 2017 ; Vol. 23, No. 1. pp. 61-79.
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