Abstract
This paper shows that the problem of decomposing a finite function f(A,B) into the form h(g(A),B), where g is a Boolean function, can be resolved in polynomial time, with respect to the size of the problem. It is also shown that omission of the characteristic of the g function can significantly complicate the problem. Such a general problem belongs to the NP-hard class of problems. The work shows how the problem of decomposition of a finite function can be reduced to the problem of coloring the vertices of a graph. It is also shown that the problem of decomposition of relations can be reduced to coloring the vertices of their hypergraphs. In order to prove the validity of the theorems, combinatory properties of Helly are used.
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