Recurrent correlations for unreliabilities of circuits in the basis consisting of Webb functions, in $P_4$ and $P_5$

Background. Multivalued logic offer broad opportunities for development of various algorithms in many field and it is successfully applied when solving various problems and in many technical developments. This explains the interest towards the problem of reliability improvement of circuits in the complete finite basis consisting of $k$-valued functions ($k \ge 3$). This article is aimed at building circuits that can be used for reliability improvement in the basis consisting of Webb functions with $k$ being 4 and 5, as well at obtaining recurrent correlations for unreliabilities of the suggested circuits and the original circuit. Materials and methods. In the course of the study, well-known methods of discrete mathematics and mathematical cybernetics were used. Besides, new methods for synthesing circuits consisting of unreliable functional gates have been suggested, as well as a new approach to obtaining circuit unreliability values. Results. In the basis consisting of Webb functions, there have been obtained the following results: 1. The author has built circuits that can be used to implemented to improve reliability of original circuits in $P_4$ and $P_5$. 2. The author has obtained recurrent correlations for unreliabilities of the suggested circuits and the original circuit.