期刊名称：Eastern-European Journal of Enterprise Technologies
印刷版ISSN：1729-3774
电子版ISSN：1729-4061
出版年度：2017
卷号：1
期号：4
页码：30-40
DOI：10.15587/1729-4061.2017.90917
语种：English
出版社：PC Technology Center
摘要：A widespread application of neural network circuits from neural elements with a threshold activation function would be possible if efficient methods for the verification of realizability of functions of the algebra of logic by one neural element are devised, as well as the synthesis of these elements with a large number of inputs. The article examines algebraic structure of kernels and reduced kernels of Boolean functions. A connection is established between the kernels of Boolean functions that are implemented by one neural element with a threshold activation function and tolerance matrices. Based on the convex linear combination of kernel elements of functions of the algebra of logic, we proved a criteria of their realizability by one neural element with a threshold activation function. By using algebraic properties of kernels in Boolean functions and the representations of their reduced kernels by tolerance matrices, we obtained a number of easily verified necessary conditions for the realizability of functions of the algebra of logic by one neural element. These necessary conditions in many cases make it possible not to perform complicated calculations by the methods of approximation of different orders and by the iterative methods, in which, by means of limit cycles, the realizability or non-realizability of Boolean functions by one neural element with a threshold activation function is determined. Based on the sufficient conditions, obtained in the work, for the realizability of functions of the algebra of logic by one neural element, we devised an effective method for the synthesis of integer neural elements with a large number of inputs.
关键词：tolerance matrix;convex linear shell;structure vector;activation function
