解布尔方程通过原子分解成独立的开关方程

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
A. Balamesh, A. Rushdi
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引用次数: 4

摘要

摘要:本文考虑在有限(原子)布尔代数上求解布尔方程组的问题,而非二值布尔代数,这里称为“大”布尔代数。本文提出了用单个布尔方程代替该方程组,并提出了将该方程组的原子分解为多个独立的开关方程来求解该方程组的新方法。该方法具有许多优点,包括以类似于最近开发的置换加性形式的形式有效地推导所有特解的完全紧表,但以更直接的方式获得而不使用参数。用许多详细的实例来说明所提出的新方法。这些示例演示了一致性条件如何将底层布尔代数分解为子代数,以及如何在非常小的空间中列出大量的特解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solution of Boolean equations via atomic decomposition into independent switching equations
ABSTRACT This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one, referred to herein as a ‘big’ Boolean algebra. The paper suggests the replacement of this system of equations by a single Boolean equation, and then proposes a novel method for solving this equation by using its atomic decomposition into several independent switching equations. This method has many advantages including the efficient derivation of a complete compact listing of all particular solutions in a form similar to the recently developed permutative additive form, but obtained in a more direct fashion without using parameters. Many detailed examples are used to illustrate the proposed new method. The examples demonstrate how the consistency condition might force a collapse of the underlying Boolean algebra into a subalgebra, and also how to list a huge number of particular solutions in a very small space.
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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