Synthesis of Logical Systems of Given Activity

A system observed from the outside as a black box displays certain activity which can be described (and stored) as variations of the input and output variables of the system during its observation. Such information stored for adequately large intervals of time represents samples of activity ready for statistical analysis. Any time-invariant obtained as a result of this investigation represents an element of behavior of the system which can be explained by the existence of corresponding elements of the internal structure of the black box. The resulting abstract model of the internal structure is algorithmic when the elements of behavior take on the form of a law predicting the future activity from some stored information about the past activity. Not all systems are found to be algorithmic. The activity of any part of an electronic digital system with a central clocking can be defined by Boolean variables arranged in suitable timetables. Any time-invariant Boolean equation holding between these variables represents an element of the system´s behavior but does not necessarily contain any algorithmic element of the system. In this paper we show how to make tests of the activity proving the existence of algorithmic elements, their synthesis and the design of corresponding block diagrams of the system.