On Complexity of Deterministic and Nondeterministic Decision Trees for Decision Tables with Many-Valued Decisions from Closed Classes

Decision trees (DTRs) and decision rules are extensively examined and applied in various domains of computer science. The theory of DTRs and rules highlights several crucial inquiries, such as how the complexity of deterministic decision trees (DDTRs) and decision rule systems depends on the complexity of the set of attributes associated with the columns of the decision table (DT). In this research paper, we focus on the analysis of nondeterministic decision trees (NDTRs) as a substitute for decision rule systems. NDTRs can be seen as representations of decision rule systems. We examine classes of DTs featuring multi-valued decisions (known as multi-label DTs) that maintain closure under attribute removal (columns) and modifications to the sets of assigned decisions for rows. We examine the behavior of functions that describe the worst-case dependence of the minimum complexity of DDTRs and NDTRs on the complexity of the set of attributes associated with the columns of tables belonging to a closed class (CC) of DTs closed under the above two operations. We enumerate all possible types of behavior exhibited by these functions.