The representation of discrete functions by decision trees: aspects of complexity and problems of testing

One such model, called a decision tree, is introduced; it is essentially a sequential evaluation procedure where, at each step, a variable's value is determined and the next action chosen accordingly. Decision trees have been used in switching circuits, data bases, pattern recognition, machine diagnosis, and remote data processing. The activity of a variable, a new concept that measures the contribution of a variable to the complexity of a function, is defined and its relation to decision trees is described. Based upon these results (which can be generalized to recursive functions and hierarchies of relations), a complexity measure is proposed. The use of that measure and of the concept of activity in testing large systems (where a number of variables may be inaccessible) is then examined, with particular emphasis on continuous checking of systems in operation.