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Decision lists and decision trees are two models of computation for boolean functions. Blum has shown (Information Processing Letters 42 (1992), 183-185) that rank-k decision trees are a subclass of decision lists. Here we identify precisely, by giving a syntactical characterization, the subclass of decision lists which correspond exactly to the class of bounded rank decision trees. Furthermore we give a more general algorithm to recover reduced decision trees from decision lists.

A syntactic characterization of bounded-rank decision trees in terms of decision lists