Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes

TL;DR

This paper investigates the relationships between the complexity of decision tables and the minimal sizes of deterministic and nondeterministic decision trees, focusing on classes closed under specific operations and classifying their interrelations.

Contribution

It provides a classification of seven relationship types among decision table complexity and minimal decision tree complexities, enriching understanding of their interplay.

Findings

Seven types of relationships classified among decision table parameters.

Enumeration of all possible relationship types.

Insights into the complexity of decision trees for specific classes.

Abstract

In this paper, we consider classes of decision tables with many-valued decisions closed under operations of removal of columns, changing of decisions, permutation of columns, and duplication of columns. We study relationships among three parameters of these tables: the complexity of a decision table (if we consider the depth of decision trees, then the complexity of a decision table is the number of columns in it), the minimum complexity of a deterministic decision tree, and the minimum complexity of a nondeterministic decision tree. We consider rough classification of functions characterizing relationships and enumerate all possible seven types of the relationships.