Efficient Modeling of Deterministic Decision Trees for Recognition of Realizable Decision Rules: Bounds on Weighted Depth

In this paper, an efficient algorithm for modeling the operation of a DDT (Deterministic Decision Tree) solving the problem of realizability of DRs (Decision Rules) is proposed and analyzed. For this problem, it is assumed that a DRS (Decision Rule System) is given; for an arbitrary tuple of feature values, it is required to recognize whether there is a DR realizable on this tuple, i.e., a DR for which the left-hand side is true on the tuple. It is shown that the weighted depth of the modeled DDT does not exceed the square of the minimum weighted depth of the NDT (Nondeterministic Decision Tree) solving the realizability problem.