Developing an algorithm to minimize boolean functions for the visual-matrix form of the analytical method

Abstract

This research has established the possibility of improving the effectiveness of the visual-matrix form of the analytical Boolean function minimization method by identifying reserves in a more complex algorithm for the operations of logical absorption and super-gluing the variables in terms of logical functions. An improvement in the efficiency of the Boolean function minimization procedure was also established, due to selecting, according to the predefined criteria, the optimal stack of logical operations for the first and second binary matrices of Boolean functions. When combining a sequence of logical operations using different techniques for gluing variables such as simple gluing and super-gluing, there are a small number of cases when function minimization is more effective if an operation of simply gluing the variables is first applied to the first matrix. Thus, a short analysis is required for the primary application of operations in the first binary matrix. That ensures the proper minimization efficiency regarding the earlier unaccounted-for variants for simplifying the Boolean functions by the visual-matrix form of the analytical method. For a series of cases, the choice of the optimal stack is also necessary for the second binary matrix. The experimental study has confirmed that the visual-matrix form of the analytical method, whose special feature is the use of 2-(n, b)-design and 2-(n, x/b)-design systems in the first matrix, improves the process efficiency, as well as the reliability of the result of Boolean function minimization. This simplifies the procedure of searching for a minimal function. Compared to analogs, that makes it possible to improve the productivity of the Boolean function minimization process by 100‒200 %. There is reason to assert the possibility of improving the efficiency of the Boolean function minimization process by the visual-matrix form of the analytical method, through the use of more complex logical operations of absorbing and super-gluing the variables. Also, by optimally combining the sequence of logical operations of super-gluing the variables and simply gluing the variables, based on the selection, according to the established criteria, of the stack of logical operations in the first binary matrix of the assigned function