球面特征函数的极小接触电路

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-12-01 DOI:10.1515/dma-2021-0036

N. P. Redkin

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引用次数: 1

摘要

摘要研究了用接触电路实现球体特征函数的复杂性。通过以顶点为中心的球的特征函数σn = (σ1，…，σn)， σ1，…，σn∈{0,1}，我们指的是布尔函数φσ (n) $\begin{array}{} \varphi^{(n)}_{\tilde\sigma} \end{array} $ (x1，…，xn)在且仅在与元组σn只相差一位的元组上等于1。结果表明，对于φσ (n) $\begin{array}{} \varphi^{(n)}_{\tilde\sigma} \end{array} $ (x)的实现，3n−2个触点的个数是充分必要的。

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Minimal contact circuits for characteristic functions of spheres

Abstract We study the complexity of implementation of the characteristic functions of spheres by contact circuits. By the characteristic functions of the sphere with center at a vertex σ̃ = (σ1, …, σn), σ1, …, σn ∈ {0, 1}, we mean the Boolean function φσ~(n) $\begin{array}{} \varphi^{(n)}_{\tilde\sigma} \end{array} $(x1, …, xn) which is equal to 1 on those and only those tuples of values that differ from the tuple σ̃ only in one digit. It is shown that the number 3n − 2 of contacts is necessary and sufficient for implementation of φσ~(n) $\begin{array}{} \varphi^{(n)}_{\tilde\sigma} \end{array} $(x̃) by a contact circuit.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.