Bounds on depth of decision trees derived from decision rule systems with discrete attributes

Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of relationships between these two models is an important task of computer science. It is easy to transform a decision tree into a decision rule system. The inverse transformation is a more difficult task. In this paper, we study unimprovable upper and lower bounds on the minimum depth of decision trees derived from decision rule systems with discrete attributes depending on the various parameters of these systems. To illustrate the process of transformation of decision rule systems into decision trees, we generalize well known result for Boolean functions to the case of functions of k-valued logic.