Rank-r Decision Trees are a Subclass of r-Decision Lists

Rivcst [5] defines the notion of a decision list as a representation for Boolean functions. He shows that k-decision lists, a generalization of k-CNF and k-DNF formulas, are learnable for constant k in the PAC (or distribution-free) learning model [&,3]. Ehrenfcucht and Haussler [l] define the notion of the rank of a decision tree, and prove that decision trees of constant rank are also learnable in the PAC model, using a more complicated algorithm. In this note, we prove that any concept (Boolean function) that can be described as a rank-r decision tree can