On tree representation of read-once functions in extended elementary bases

Background. The mathematics of Booleand functions has a profound effect in the area of information technologies. This article is devoted to an important ability of the function to be represented in the given basis via a formula without replication of variables (a read-once formula). Functions which can be represented such way may be regarded as quite simply structured in this basis. We consider a problem of read-once functions' tree representation in the bases consisting of conjunction, disjunction, negation and polarized Stecenko's functions. The object of the article is to provide a tree representation where equal functions have isomorphic trees and obtain a set of relevant equivalent tree transformations. Materials and methods. We apply the mathematics of permutations and use properties of polirized Stecenko's functions and labeled rooted trees. Results and conclusion. We have provided a tree representation for read-once functions in the bases consisting of polarized Stecenko's functions and an elementary basis aand corresponding to formulas with raised negotiations, as well as obtained a set of relevant equivalent transformations for the given type of trees.