IMPLEMENTATION OF A NON-STANDARD SYSTEM FOR SIMPLIFYING PEIRCE-WEBB FUNCTIONS

Solomko M. and Tadeyev P. and Antoniuk M. and Mala Y. and Babych S. and Ivashchuk Y. (2024) IMPLEMENTATION OF A NON-STANDARD SYSTEM FOR SIMPLIFYING PEIRCE-WEBB FUNCTIONS. Eastern-European Journal of Enterprise Technologies, 2024 (№5/4): 131. pp. 6-32. ISSN 1729-3774

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Abstract

The object of research are models of optimal logic circuits based on universal Peirce-Webb functions. The problem solved is the efficiency of the technique for simplifying the Peirce-Webb functions. The extension of the non-standard system to the simplification of Peirce-Webb functions makes it possible to discover new rules of equivalent transformations of Boolean functions, and to complete the simplification procedure in one step. A feature of the simplification of functions in the Peirce-Webb basis by a non-standard system is fixing the digital project at the level of abstraction, followed by the application of the mechanism of logical synthesis to generate the corresponding equivalent at the level of gates of the logic circuit. The result of the transformation of the terms of the binary matrix in the end is some combinatorial system, metadata that can explain other data, for example, determine the minimum function for another logical basis.
The interpretation of the result consists in the use of combinatorial properties of binary structures of functions in the Peirce-Webb basis and binary structures of functions in the basic basis. These roperties do not depend on the selected logical basis, which makes it possible to carry out equivalent transformations on binary matrices of Peirce-Webb functions according to the rules of the algebra of the main basis.
It has been experimentally confirmed that a nonstandard system enables:
– to reduce the algorithmic complexity of simplifying the Peirce-Webb functions;
– to increase the performance of the simplification of Peirce-Webb functions by 200–300 %;
– to demonstrate the visibility of the process of simplifying functions.
In terms of application, the non-standard system of simplifying the Peirce-Webb functions could ensure the transfer of innovations to material production: from conducting fundamental research, expanding the capabilities of digital component design technology to organizing serial or mass production of novelties.

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