About the improvement of the method of variables selection when solving logical equations.

In the paper [1], for the solution of Boolean equations of the form $F\left ( x_{1},x_{2},...,x_{k_{0}} \right )=1$ the method for allocation of variables was offered. This work aims at improving the efficiency of this method due to a decrease of the maximum volume of the intermediate forms which are obtained in the process of the variables selection. This result is achieved by: 1) combining some elements of a disjunctive forms of the original superposition of functions $F$ before their logical multiplication and 2) rejection of the substitution or simplification of the form substitute the disjunctive forms of functions that do not affect the formation of zeroconjunction $x_{u}\bar{x}_{u}$ when DNF is received of a function $F$. It is shown that the amount of memory required to allocate the final DNF can be reduced by forming one or some of its members from a bracket the shape of the function $F$ obtained after selection of all variables that form when the transformation of the original set of functions in DNF at least one zero-conjunction $x_{u}\bar{x}_{u}$ $\left ( u\in \left \{ 1,2,...,k_{0} \right \} \right )$.Introduced more efficient than presented in [1] criterion for variable selection determining the next stage of decomposition of the original problem.

Keywords: Logical Equations, Separation of Variables, Decomposition of the Problem.