The algebraic properties of cores of generalized neurofunctions / Geche, / Mulesa. (2018)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2018, 54 (6))

Geche F., Mulesa O.
The algebraic properties of cores of generalized neurofunctions

This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: character of a group, core of a function, generalized neural element, spectrum of a function, synthesis, tolerance matrix, Boolean functions, Computer circuits, Synthesis (chemical), Algebraic properties, Algebraic structures, character of a group, Information compression, Methods of synthesis, Neural element, Tolerance matrixes, Transmission problem, Matrix algebra


Cite:
Geche F., Mulesa O. (2018). The algebraic properties of cores of generalized neurofunctions. Cybernetics and Systems Analysis, 54 (6), 27-36. doi: https://doi.org/10.1007/s10559-018-0090-4 http://jnas.nbuv.gov.ua/article/UJRN-0000926950 [In Ukrainian].


 

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