Continuous semiring-semimodule pairs and mixed algebraic systems

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...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerzők: Ésik Zoltán
Kuich Werner
Dokumentumtípus: Cikk
Megjelent: 2017
Sorozat:Acta cybernetica 23 No. 1
Kulcsszavak:Algebra, Félcsoport - algebra
Tárgyszavak:
Online Access:http://acta.bibl.u-szeged.hu/50063
Leíró adatok
Tartalmi kivonat: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.
Terjedelem/Fizikai jellemzők:061-079
ISSN:0324-721X