Deterministic and Strongly Nondeterministic Decision Trees for Decision Tables from Closed Classes

TL;DR

This paper investigates the complexity of deterministic and strongly nondeterministic decision trees for decision tables within closed classes, analyzing how various parameters influence their minimal complexity.

Contribution

It introduces a detailed analysis of the minimal complexity of decision trees in closed classes, highlighting the dependence on test complexity, attribute set complexity, and nondeterminism.

Findings

Complexity bounds for deterministic decision trees are established.

Dependence of nondeterministic decision tree complexity on attribute set complexity is characterized.

Results provide insights into the structure of decision trees for closed classes of decision tables.

Abstract

In this paper, we consider classes of decision tables with 0-1-decisions closed relative to removal of attributes (columns) and changing decisions assigned to rows. For tables from an arbitrary closed class, we study the dependence of the minimum complexity of deterministic decision trees on various parameters of the tables: the minimum complexity of a test, the complexity of the set of attributes attached to columns, and the minimum complexity of a strongly nondeterministic decision tree. We also study the dependence of the minimum complexity of strongly nondeterministic decision trees on the complexity of the set of attributes attached to columns. Note that a strongly nondeterministic decision tree can be interpreted as a set of true decision rules that cover all rows labeled with the decision 1.