In this paper, we study the problems of finding minimal tests, testers, and a set of variables that are essential for not everywhere defined functions. Such problems are discrete extremal problems of one class, and in algorithms that implement methods for solving them, at each step, a set of variables of not everywhere defined functions is selected. We prove a theorem on the equivalence of the search problems for minimal tests, testers and a set of variables that are essential for not everywhere defined functions, the problem of finding the maximum upper zero of monotone Boolean functions.