Comparison of Complexity of Regular Versus Oblivious Decision Trees for Decision Tables With Many-Valued Decisions From Closed Classes

In this work, we examine decision table (DTA) classes that are closed in terms of decision modification (i.e., the sets of decisions) and attribute deletion (i.e., columns). We examine the relationship between the minimum complexity of regular decision trees (DTRs) and the minimum complexity of oblivious DTRs, where the order of queries on attribute values is preset, for tables belonging to these classes. We show (and this is the main novelty of the paper) that the function expressing this dependence either grows logarithmically, or develops almost linearly, or is bounded from above by a constant. The depth and weighted depth of DTRs are examples of so-called bounded complexity measures (BCMs) for which this result is valid. Furthermore, for a DTA, we show that the minimum complexity of a reduct for that table is equal to the minimum complexity of an oblivious DTR.