On a circuit that increases reliability in the basis consisting of a Webb function, at $P_{k}$

Background. Multivalued logic opens broad opportunities to develop various algorithms in many fields. It is successfully implied for solving multiple problems and in many technical developments. This explains the interest in the problem of increasing the efficiency of circuits in the complete finite basis consisting of $k$-valued functions ($k \geq 3$). The aim of the article is to build circuits suitable for increasing reliability in the basis consisting of a Webb function at random $k$, as well as to obtain recurrent correlations for unreliabilities of the suggested circuits and the initial circuit. Materials and methods. The work uses well-known methods of discrete mathematics, mathematical cybernetics and mathematical analysis. Besides, the article suggests new methods for synthesizing circuits consisting of unreliable functional gates, as well as new approaches to obtaining circuit unreliability estimates. Results. The author has obtained the following results for the basis consisting of a Webb function: 1. One has obtained the circuits suitable for increasing reliability of initial circuits at $P_{k}$. 2. One has obtained recurrent correlations for unreliabilities of the suggested circuits and the initial circuit.