On closed classes in partial k-valued logic that contain the class of monotone functions
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Valeriy B. Alekseev
Abstract
Let A be a precomplete class (a maximal clone) in k-valued logic and T(A) be the family of all closed classes (under superposition) in partial k-valued logic that contain A. A simple test is put forward capable of finding out from a partial order defining the precomplete class A of monotone functions whether the family T(A) is finite or infinite. This completes the solution of the problem of finiteness of T(A) for all precomplete classes of k-valued logic. The proof depends on new families of closed classes founded by the author of the present paper.
Funding
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 17-01-00782-a).
Originally published in Diskretnaya Matematika (2018) 30, №2, 3–13 (in Russian).
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
