Mathematics & Physics 2016, 9(1), 119–122 УДК 519.716 On Decomposition of Sub-definite Partial Boolean Functions Ivan K. Sharankhaev∗ Institute of Mathematics and Computer Science Buryat State University Smolin, 24a, Ulan-Ude, 670000 Russia Received 02.11.2015, received in revised form 06.12.2015, accepted 15.01.2016 In this article we study Boolean functions with two kinds of indeterminacy. <...> We prove criterion of decomposition of this functions including separating decomposition. <...> As a result we have method that allows to obtain representation of an arbitrary function using superposition of functions that have smaller dimentions. <...> Keywords: incompletely defined Boolean function, sub-definite partial Boolean function, decomposition, superposition. <...> Introduction In the theory of discrete functions rapidly developing area, is engaged study of functions defined on a finite set A and receiving as their values subsets of A, including ∅. <...> Such maps are found in the mathematical modeling of information processing, in the case where the set A = {0, 1} are incompletely defined Boolean functions. <...> As can be seen, there are two kinds of indeterminacy. <...> For the first type of indeterminacy on the sets on which the function value is not defined, the indeterminacy is understood as the ability to adopt and value 0 and value 1, i.e. image of these sets is the set {0, 1}. <...> The second type of indeterminacy are associated with the empty set, typically means taboo data and studied, for example, in [2]. <...> In this paper we consider incompletely defined Boolean functions with two kinds of indeterminacy, following [3], we call them sub-definite partial Boolean functions. <...> The problem of representation of an arbitrary sub-definite partial Boolean function by the functions of lower dimension is very important. <...> We proved criterion of decomposition subdefinite partial Boolean functions, including separating decomposition, which generalizes the criterion of the functional separability of Boolean functions by G. N.Povarov [4] and provides a method of obtaining representations sub-definite partial Boolean functions by the functions of lower dimension. <...> The work [5] is dedicated to finding of repetition-free representations of sub-definite partial Boolean functions in a special basic set. <...> We note that the obtaining of the results of [5 <...>