Continuous semiring-semimodule pairs and mixed algebraic systems

Ésik Zoltán and Kuich Werner: Continuous semiring-semimodule pairs and mixed algebraic systems. In: Acta cybernetica, (23) 1. 061-079. (2017)

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We associate with every commutative continuous semiring S and alphabet Σ 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 S⟪(Y⊎Σ)*⟫ of finite words over Y⊎Σ, an X × Y -matrix over S⟪(Y⊎Σ)*⟫, and a function from into the continuous S⟪(Y⊎Σ)*⟫-semimodule S⟪(Y⊎Σ)ω⟫ of series of ω-words over Y⊎Σ. 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 ω-words.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2017
Volume: 23
Number: 1
ISSN: 0324-721X
Page Range: 061-079
Language: English
Place of Publication: Szeged
Related URLs:
Uncontrolled Keywords: Algebra, Félcsoport - algebra
Additional Information: Bibliogr.: 79. p. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2018. Feb. 12. 08:48
Last Modified: 2022. Jun. 20. 15:51

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