Implementing the method of figurative transformations to minimize partially defined Boolean functions

Authors

DOI:

https://doi.org/10.15587/1729-4061.2023.273293

Keywords:

minimization of partially defined Boolean functions by the method of figurative transformations, location of equivalent transformations

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 visual-matrix form of the analytical method still has the prospect of increasing its hardware capabilities, including in terms of minimizing partially defined Boolean functions.

It has been experimentally confirmed that the method of figurative transformations increases the efficiency of minimizing partially defined Boolean functions, compared with analogs, by 100–200 %.

There is reason to argue about the possibility of increasing the efficiency of minimizing partially defined Boolean functions in the main and polynomial bases by the specified method. The effectiveness of the method, in particular, is ensured by carrying out all operations of generalized gluing of variables for dead-end disjunctive normal forms (DNF), followed by the use of implicant tables; optimal combination of a sequence of logical operations for gluing variables

Author Biographies

Mykhailo Solomko, National University of Water and Environmental Engineering

PhD, Associate Professor

Department of Computer Engineering

Mykola Antoniuk, Rivne State University of Humanities

PhD, Associate Professor

Department of Information and Communication Technologies and Methods of Teaching Informatics

Ihor Voitovych, Rivne State University of Humanities

Doctor of Pedagogical Sciences, Professor

Department of Information and Communication Technologies and Methods of Teaching Informatics

Yuliia Ulianovska, University of Customs and Finance

PhD, Associate Professor

Department of Computer Science and Software Engineering

Nataliia Pavlova, Rivne State University of Humanities

PhD, Associate Professor

Department of Information and Communication Technologies and Methods of Teaching Computer Science

Viacheslav Biletskyi, Rivne State University of Humanities

PhD, Associate Professor

Department of Information and Communication Technologies and Methods of Teaching Computer Science

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Implementing the method of figurative transformations to minimize partially defined Boolean functions

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Published

2023-02-28

How to Cite

Solomko, M., Antoniuk, M., Voitovych, I., Ulianovska, Y., Pavlova, N., & Biletskyi, V. (2023). Implementing the method of figurative transformations to minimize partially defined Boolean functions. Eastern-European Journal of Enterprise Technologies, 1(4 (121), 6–25. https://doi.org/10.15587/1729-4061.2023.273293

Issue

Vol. 1 No. 4 (121) (2023): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2023 Mykhailo Solomko, Mykola Antoniuk, Ihor Voitovych, Yuliia Ulianovska, Nataliia Pavlova, Viacheslav Biletskyi

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