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Mappings with Coenumerable Graphs. / Morozov, A. S.
в: Algebra and Logic, Том 63, № 6, 01.2025, стр. 448-457.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Mappings with Coenumerable Graphs
AU - Morozov, A. S.
N1 - Morozov, A.S. Mappings with Coenumerable Graphs. Algebra Logic 63, 448–457 (2025). https://doi.org/10.1007/s10469-025-09805-1 The work was supported by the basic project of No. FWNF 2022–0012.
PY - 2025/1
Y1 - 2025/1
N2 - We study partial mappings on natural numbers, the graphs of which are coenumerable. Such mappings are referred to as negative mappings. We show that any 0′-computable partial function is represented as the superposition of two negative ones. We also show that the inverse semigroup of all 0′-computable partial injective mappings is generated by its negative elements; moreover, any its element is equal to the product of its two negative elements. We show that the group of all 0′-computable permutations is generated by its negative elements. We obtain sufficient conditions for the representability of 0′- computable permutations in the form of the superposition of two negative permutations.
AB - We study partial mappings on natural numbers, the graphs of which are coenumerable. Such mappings are referred to as negative mappings. We show that any 0′-computable partial function is represented as the superposition of two negative ones. We also show that the inverse semigroup of all 0′-computable partial injective mappings is generated by its negative elements; moreover, any its element is equal to the product of its two negative elements. We show that the group of all 0′-computable permutations is generated by its negative elements. We obtain sufficient conditions for the representability of 0′- computable permutations in the form of the superposition of two negative permutations.
KW - computability
KW - computable permutation
KW - graph
UR - https://www.scopus.com/pages/publications/105020871692
UR - https://www.mendeley.com/catalogue/0b0c25e0-25bc-3ff7-ba48-0aad71a417e8/
U2 - 10.1007/s10469-025-09805-1
DO - 10.1007/s10469-025-09805-1
M3 - Article
VL - 63
SP - 448
EP - 457
JO - Algebra and Logic
JF - Algebra and Logic
SN - 0002-5232
IS - 6
ER -
ID: 72580904