Ésik Zoltán and Kuich Werner: Continuous semiring-semimodule pairs and mixed algebraic systems. In: Acta cybernetica, (23) 1. 061-079. (2017)
Preview |
Cikk, tanulmány, mű
actacyb_23_1_2017_5.pdf Download (470kB) | Preview |
Abstract
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: | http://acta.bibl.u-szeged.hu/50021/ |
| 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 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/50063 |
Actions (login required)
 |
View Item |
