On the complexity of implementation of a system of three monomials of two variables by composition circuits
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Sergey A. Korneev
Abstract
We study the complexity of implementation of systems of monomials by composition circuits. Here, by the complexity we mean the smallest possible number of operations required for computation of the system of monomials from the variables; under this approach, results of intermediate computations can be used several times. The main result of this paper establishes, for an arbitrary system of three monomials of two variables without zeroth powers, a formula for the complexity of their joint implementation by composition circuits with an additive error which is either 1 or 0.
Originally published in Diskretnaya Matematika (2022) 34, №4, 36–51 (in Russian).
Funding statement: This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of a program of the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2022-284).
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements
- On the approximation of high-order binary Markov chains by parsimonious models
- On the complexity of implementation of a system of three monomials of two variables by composition circuits
- Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model
- Inverse homomorphisms of finite groups
Artikel in diesem Heft
- Frontmatter
- Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements
- On the approximation of high-order binary Markov chains by parsimonious models
- On the complexity of implementation of a system of three monomials of two variables by composition circuits
- Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model
- Inverse homomorphisms of finite groups
