THE EQUATIONS, OPERATORS IN PROGRAMS SPACES AND COMPLEXITY ASSESSMENT
In the work some formal mathematical operators and the operator equations in programs sets are probed. It is useful in case of creation and a research of the formal programs therefore it is researched their properties. Also a problem of complexity of programs and solutions of the program equations are probed. Operators of minimization on quantity of operands, operators, time of programming of the program is probed, their functional properties are studied (from the point of view of the mathematical functional analysis). Existence and uniqueness of a stationary point of operators, their linearity, homogeneity, a monotonicity are probed. We consider the actual volume and boundary volume of the program without communications with a certain programming language. Are systemically researched a problem of complexity of programs. The complexity happens different type, different form, but in article we are interested only in the form. In particular, programs which are representation the oriented graph, a tree and vectorial function. Depending on the variables used in the program the appropriate analysis is made. In the latter case length is determined by quantity of global variables, and we estimate complexity of the program as the amount of its components. The complexity of programs is set by axioms (according to the general systems theory), the effective didactic example is this. Results will help to formalize, construct the system of assessment of programs, to execute their check, to increase relevance, to reduce complexity of programs.