id: 37279
Title: The theoretical basis overview for substantiating and choosing the ways and principles of building multi-valued logic computing systems
Authors: Krasilenko V.G., Dubchak V.M., Diachynska O.M.
Keywords: multi-valued logic, threshold logic, parallel processing, accelerator, non-traditional mathematical apparatus, multi-valued computing system, multilinearly separable function, universal picture elements of matrix two-valued and multi-valued logic
Date of publication: 2024-10-17 09:48:41
Last changes: 2024-10-17 09:48:41
Year of publication: 2024
Summary: The article is devoted to the review and analysis of the theoretical basis and mathematical apparatus of some unconventional, less well-known and much less often used logics, including scalar threshold and multivalued logics, especially matrix logics, which are a generalization of scalar logics and significantly expand their functionality compared to scalar logics. Special attention is paid to the review of linearly and monotonically multilinearly separable functions, which can be a theoretical basis for the synthesis of logical elements based on them with corresponding k-valued alphabets, with sign-variable codes, or non-positional coding systems, for example, with a system of coding residues. On the basis of the analysis of this mathematical basis, justification was made and possible promising ways of building multi-valued logic computing systems were selected. It is proved that the use of monotonically multilinearly separable functions and more general multivalued or threshold logics allows the synthesis and development of functionally more powerful computing devices and systems of multivalued logic to be reduced to the development of a parallel array of logical elements of multivalued logic based on modulo addition operations and the use of systems residual coding. The need to create universal or quasi-universal picture logic elements of matrix two-value logic with a programmable setting for the performed function is formulated, since they can become the main hardware basis for devices of multi-value and neural, and especially matrix logic. Selected on the basis of a review and analysis of both the theoretical basis and achievements in optoelectronics, promising ways and principles of building promising multi-valued logic computing systems, the hardware basis of which can be multi-threshold comparator-selectors, implemented including on the basis of current reflectors and photonic elements of integrated optics.
URI: http://socrates.vsau.edu.ua/repository/getfile.php/37279.pdf
Publication type: Статті у наукових фахових виданнях України (Copernicus та інші)
Publication: Наука і техніка сьогодні. 2024. № 9 (37). С. 531-545. URL: http://perspectives.pp.ua/index.php/nts/article/view/15102/15172 DOI: https://doi.org/10.52058/2786-6025-2024-9(37)
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