Vector Models for Modeling Logic Based on XOR-Relations

A model of relations between logical functions is proposed, which are used for the synthesis of digital circuits. Relation structures use the XOR-operation, which allows solving problems of technical diagnostics, such as creating fault models, fault modeling, test synthesis, evaluation of their quality, and diagnosis of single and multiple constant defects. A method for the synthesis of deductive formulas based on the use of binary vectors to describe the behavior of logical elements is proposed. Methods for deductive analysis of digital elements based on the use of tabular, analytical and vector models are proposed. Examples of constructing deductive formulas for modeling faults on test sets are given. Estimates of the computational complexity of the methods are given in order to demonstrate the advantages of vector data structures and the corresponding method of deductive analysis.