Complexity of Deterministic and Strongly Nondeterministic Decision Trees for Decision Tables with 0-1-Decisions from Closed Classes

In this chapter, 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. One can interpret strongly nondeterministic decision trees for a decision table as a way to represent an arbitrary system of true decision rules for this table that cover all rows labeled with the decision 1.