On the computational power of boolean decision lists

Abstract

We study the computational power of decision lists over AND-functions versus threshold-⊕ circuits. AND-decision lists are a natural generalization of formulas in disjunctive or conjunctive normal form. We showthat, in contrast to CNF- and DNF-formulas, there are functions with small AND-decision lists which need exponential size unbounded weight threshold-⊕ circuits. This implies that Jackson’s polynomial learning algorithm for DNFs [7] which is based on the efficient simulation of DNFs by polynomial weight threshold-⊕ circuits [8], cannot be applied to AND-decision lists. A further result is that for all k ≥ 1 the complexity class defined by polynomial length ACk0-decision lists lies strictly between ACk0+1 and ACk0+2.