Abstract. In this paper, we consider generalized neural elements and study the conditions for the implementation of the functions of the algebra of logic with such elements. The concept of a modified core of Boolean functions is introduced in relation to the systems of groups’ character where the functions of the algebra of logic are defined. The criteria for belonging these functions to a class of generalized neural functions are given. The algebraic structure of the core of Boolean neurofunctions is investigated and number of necessary conditions for the implementation of Boolean functions by one generalized neural element are established based on the properties of tolerance matrices. The received results allow elaborating efficient methods of synthesis of integer generalized neural elements with many inputs, which can be used in problems of information compression and transmission and discrete signal recognition.
Keywords: generalized neural element, core of function, function's spectrum, group character, synthesis, tolerance matrix.