Abstract
The decomposition of a complex system is one of the very important problems of systems theory. In this paper we consider the following problem of the decomposition: Given a global system S⊂X×Y and a class of component subsystems {Si⊂Xi×Yi|i=1, 2, …, n}. Find a necessary and sufficient condition when there exists a complex systm representation S⊂S1×S2…×Sn such that S is related to S by surjective modelling morphism.
A surjective modelling morphism h: S→S yields an approximation of the global system S in some sense.
In the above problem the complex system representation S is not specialized but can be a general input output system. Problems of practical interest, however, usually require the complex system representation to satisfy some specific properties. As a corollary of the above cosideration, therefore, we also treat the case when the complex system representation S is a non-interactede system such that S=S1 ×S2×…×Sn·
Finally, as an illustration of the above result we discuss “Stair Case” game which is a typical problem-solving problem of artificial intelligence.
