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<p>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 <b>0′</b>-computable partial function is represented as the superposition of two negative ones. We also show that the inverse semigroup of all <b>0′</b>-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 <b>0′</b>-computable permutations is generated by its negative elements. We obtain sufficient conditions for the representability of <b>0′</b>- computable permutations in the form of the superposition of two negative permutations.</p>

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Mappings with Coenumerable Graphs

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • A. S. Morozov

摘要

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.