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Application of Hypergraphs in the Prime Implicants Selection Process

机译：超图在素数蕴涵选择过程中的应用

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The paper presents a new concept of the selection of prime implicants in a two-level logic minimization of Boolean functions. The method is based on the two-level minimization process of the Boolean functions, according to the Quine-McCluskey approach. Initially, the set of prime implicants for the logic function ought to be calculated. Next, the selection process is applied to achieve the minimal formula. Such an operation is a typical covering problem and in general case it has exponential computational complexity. In the paper we propose a new prime implicants selection method. An idea is based on the hypergraph theory. The prime implicants matrix (chart) is formed as a selection hypergraph. If the selection hyper-graph belongs to the Exact Transversal Hypergraph class (xt-class), the solution may be obtained in a polynomial time, which is not possible in a general case. The proposed method is illustrated by an example. All necessary steps will be shown in order to apply the proposed selection algorithm to minimize an exemplary Boolean function.
机译：本文提出了在布尔函数的两级逻辑最小化中选择素数蕴涵的新概念。根据Quine-McCluskey方法，该方法基于布尔函数的两级最小化过程。最初，应该计算逻辑函数的素数集合。接下来，应用选择过程以获得最小公式。这样的操作是典型的覆盖问题，并且在一般情况下，它具有指数计算复杂性。在本文中，我们提出了一种新的主​​要蕴含物选择方法。一个想法基于超图理论。素数蕴涵矩阵（图）形成为选择超图。如果选择超图属于精确横向超图类（xt-class），则可以在多项式时间内获得解，这在一般情况下是不可能的。举例说明了所提出的方法。为了应用所提出的选择算法以最小化示例性布尔函数，将示出所有必要步骤。

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