IMPLEMENTING THE METHOD OF FIGURATIVE TRANSFORMATIONS TO MINIMIZE PARTIALLY DEFINED BOOLEAN FUNCTIONS

Solomko M. and Antoniuk M. and Voitovych I. and Ulianovska Y. and Pavlova N. and Biletskyi V. (2023) IMPLEMENTING THE METHOD OF FIGURATIVE TRANSFORMATIONS TO MINIMIZE PARTIALLY DEFINED BOOLEAN FUNCTIONS. Eastern-European Journal of Enterprise Technologies, 2023 (№1(4)): 121. pp. 6-25. ISSN 1729-3774

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Abstract

This paper reports a research that established the possibility of increasing the effectiveness of the method of figurative transformations to minimize partially defined Boolean functions. The method makes it possible, without loss of functionality, to reduce the complexity of the minimization procedure, compared to sorting out binary definitions of partially defined Boolean functions. The interpretation of the result is that the 2-(n, b)-design, 2-(n, x/b)-design systems are a reflection of logical operations. Therefore, the identification of such combinatorial systems in the truth table of logical functions directly and unambiguously establishes the location of logical operations for equivalent transformations of Boolean expressions. This, in turn, implicates an algorithm for simplifying Boolean functions, including partially defined Boolean functions.
Thus, the method of figurative transformations simplifies and speeds up the procedure for minimizing partially defined Boolean functions, compared to analogs. This indicates that the visualmatrix form of the analytical method still has the prospect of increasing its hardware capabilities, including in terms of minimizing partially defined Boolean functions.

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