关于分离接触电路类中一些初等连接系统的实现

IF 0.3 Q4 MATHEMATICS, APPLIED
Elena G. Krasulina
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引用次数: 1

摘要

摘要我们证明了初等连接系统Ωn,2k=K0,…,K2k−1$\Omega_{n,2^k}={k_0,\ldots,k_{2^{k}-1}$使得每个连接本质上依赖于n个变量并对应于线性(n,k)码的某个码字,可以通过复杂度至多为2k+1+4k(n − k) −2。我们还证明了如果一个接触(1,2k)-终端网络分离并实现了初等连接系统Ωn,2k$\Omega_{n,2^k}$,那么其中的接触数至少为2k+1−2。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On implementation of some systems of elementary conjunctions in the class of separating contact circuits
Abstract We show that the system of elementary conjunctions Ωn,2k=K0,…,K2k−1 $ \Omega_{n,2^k} = {K_0,\ldots,K_{2^{k} -1}} $ such that each conjunction depends essentially on n variables and corresponds to some codeword of a linear (n, k)-code can be implemented by a separating contact circuit of complexity at most 2k+1 +4k(n − k) − 2. We also show that if a contact (1, 2k)-terminal network is separating and implements the system of elementary conjunctions Ωn,2k $ \Omega_{n,2^k} $ , then the number of contacts in it is at least 2k+1 − 2.
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来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
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.
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