Local transformations of monotone systems. I. The problem of kernel correction in a monotone system

An accurate solution is provided of the problem of search for local changes in source data necessary and sufficient for the desired correction of the structurization result, i. e. inclusion of the specified element in the kernel of the monotone system or its elimination from the kernel [1]. For this purpose a new class of $p$-monotone system is introduced and some its properties are considered, in particular those which make it possible to solve the primal structurization problem, kernel identification,, by an algorithm which is an order of magnitude faster.