On single detection test sets under replacements of gates with inverters

Detection testing of Boolean functions implemented by Boolean circuits, which are affected by single replacements of gates with inverters, was discussed. The relevance of the study is determined by the fact that replacements of gates with inverters is a type of malfunction that occurs in the development and production of VLSI. The study was carried out in order to prove the possibility of constructing easily testable circuits under replacing elements with inverters. To achieve this goal, special methods for the synthesis of easily testable circuits were developed. Based on the results of the study, the following conclusions were drawn: for an arbitrary Boolean function implemented over a Zhegalkin basis $B_1 = \{ x\mathbin{\&} y, x\oplus y, 1\}$, there is an irredundant circuit that allows a single detection test set consisting of one vector; for an arbitrary Boolean function implemented over a standard basis $B_0=\{x\mathbin{\&}y, x\vee y, \bar x\}$, there is an irredundant circuit that allows a single detection test set consisting of two vectors.