Lower bound for the complexity of five-valued polarized polynomials
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Aleksandr S. Baliuk
and
Anna S. Zinchenko
Abstract
The paper is devoted to the complexity of representation of q-valued functions by polarized polynomials and by matrix Kronecker forms of certain type. The complexity of a function is the minimal possible number of nonzero coefficients of a polynomial or a Kronecker form representing the function. It is known that for polynomial representation and representation by Kronecker forms of a certain type the maximal values of complexity in the class of all q-valued n-ary functions coincide. We establish the lower bound of these maximal values for five-valued functions.
Originally published in Diskretnaya Matematika (2016) 28,№4, 29–37 (in Russian).
References
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Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
