On One Approach to Elimination of Weak Inequalities in the Procedure of Convolution of Systems of Linear Inequalities

The procedure for cleaning weak inequalities in the Fourier-Chernikov algorithm for convolution of a system of linear inequalities is considered. An algorithm for identifying all weak inequalities of a system based on the Gauss method for solving systems of linear equations is proposed. The algorithm requires a polynomial number of operations. It is generalized to systems of inequalities given by multilinear functions.