On the degree of restrictions of q-valued logic vector functions to linear manifolds
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Vladimir G. Ryabov
Abstract
We obtain estimates for the probability that for a randomly selected k-dimensional n-place q-valued logic vector function there exists a linear manifold of fixed dimension such that the degree of the restriction of the function to this manifold is not larger than the given value. The asymptotics of the number of manifolds on which the restrictions are affine is obtained. It is shown that if n → ∞ and k ≤ n/q, then for almost all k-dimensional n-place vector functions the maximum dimension of a manifold on which the restriction is affine lies in the interval
Note
Originally published in Diskretnaya Matematika (2020) 32,№2, 61–70 (in Russian).
References
[1] Alon N., Spencer J. H., The Probabilistic Method, Wiley, 1992.Search in Google Scholar
[2] Glukhov M.M., ElizarovV.P.,Nechaev A.A.,Algebra.V. Textbook in two volumes.V. 2,GeliosARV,Moscow, 2003 (in Russian), 416 pp.Search in Google Scholar
[3] Ryabov V. G., “On the degree of restrictions of q-valued logic vector functions to linear manifolds”, Prikladnaya diskretnaya matematika, 45 (2019), 13–25 (in Russian).10.17223/20710410/45/2Search in Google Scholar
[4] Cheremushkin A. V., “An additive approach to nonlinear degree of discrete function”, Prikladnaya diskretnaya matematika, 2010,№2(8), 22–33 (in Russian).10.17223/20710410/8/4Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Two-sided problem for the random walk with bounded maximal increment
- On the use of binary operations for the construction of a multiply transitive class of block transformations
- On the complexity of implementation of a system of two monomials by composition circuits
- On the degree of restrictions of q-valued logic vector functions to linear manifolds
- Trees with a given number of leaves and the maximal number of maximum independent sets
- Size distribution of the largest component of a random A-mapping
Articles in the same Issue
- Frontmatter
- Two-sided problem for the random walk with bounded maximal increment
- On the use of binary operations for the construction of a multiply transitive class of block transformations
- On the complexity of implementation of a system of two monomials by composition circuits
- On the degree of restrictions of q-valued logic vector functions to linear manifolds
- Trees with a given number of leaves and the maximal number of maximum independent sets
- Size distribution of the largest component of a random A-mapping
