In this chapter, various problems of recognizing properties of decision rule systems are considered. Deterministic and nondeterministic decision trees are used as solution algorithms. It is proved that the minimum depth of a deterministic decision tree solving the problem is bounded from above by the square of the minimum depth of a nondeterministic decision tree. The minimum number of nodes in deterministic and nondeterministic decision trees can grow exponentially with the size of the original rule systems. This means that, in the general case, instead of constructing the entire decision tree, its operation should be modeled on a given tuple of attribute values. We propose a greedy algorithm for such modeling and study its efficiency for a class of problems of recognizing properties of decision rule systems.