A method of synthesis of irredundant circuits (in a standard basis) admitting single fault diagnostic test sets with cardinality 2

Background. The aim of this work is to demonstrate that for an arbitrary Boolean function it is possible to construct a circuit (in the basis $\{x\&y, x\vee y, -x\}$) realizing this function and allowing a small single fault diagnosing test set (under inverse faults on outputs of gates). It can be useful for the design of easily testable VLSI. Materials and methods. The theory of Boolean functions and combinational circuits design methods were used. Results. It has been established that for arbitrary Boolean function f depending on $n$ variables there exists an irredundant combinational circuit (in the basis $\{x\&y, x\vee y, -x\}$) realizing f and admitting a single fault diagnosing test set (under inverse faults on outputs of gates) with cardinality 2 or less. For every Boolean function the minimal cardinality of a single diagnostic test set has been established.