Boolean Functions Implementation in Perception Structures

Authors

  • S. V. Yakovyn Ivano-Frankivsk National Technical University of Oil and Gas
  • S. I. Melnychuk Ivano-Frankivsk National Technical University of Oil and Gas

DOI:

https://doi.org/10.31649/1997-9266-2024-176-5-48-55

Keywords:

perceptron structures, binary signals, Boolean functions, signal processing, probabilistic characteristics

Abstract

The authors consider the peculiarities of Boolean functions realization based on perceptron structures. The limitations of the typical structure of the perceptron are determined, in particular its ability to perform only linearly separable functions, as well as main approaches to overcoming such limitations, which are solved by complicating the structures.

Attention is also paid to probabilistic features that can be used to improve the learning process of perceptrons, using probabilistic learning algorithms and higher-order probabilistic perceptrons that use Bayesian probabilities. The problems of implementing Boolean functions of higher orders are considered, including the need to use polynomials of higher orders, the complexity of learning and computational practicality. Approaches to the decomposition of Boolean functions of higher orders into a series of linearly separable functions are presented.

In addition, the capabilities of single-layer perceptrons for the classification of linearly separable objects with binary results and their limitations are analyzed. Variants of improving single-layer perceptron structures by using power functions and probabilistic signal indicators to expand their classification capabilities are described.

The obtained results confirm the relevance and perspective of further research and development of new perceptron structures for more effective solution of machine learning problems, including the development of specialized structures and learning algorithms to work with higher-order functions.

Author Biographies

S. V. Yakovyn, Ivano-Frankivsk National Technical University of Oil and Gas

Post-Graduate Student the Chair of Computer Systems and Networks

S. I. Melnychuk, Ivano-Frankivsk National Technical University of Oil and Gas

Dr. Sc. (Eng.), Professor, Head of the Chair of Computer Systems and Networks

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Published

2024-10-31

How to Cite

[1]
S. V. Yakovyn and S. I. Melnychuk, “Boolean Functions Implementation in Perception Structures”, Вісник ВПІ, no. 5, pp. 48–55, Oct. 2024.

Issue

No. 5 (2024)

Section

Information technologies and computer sciences

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