On the Read-Once Property of Branching Programs and CNFs of Bounded Treewidth

Abstract

In this paper we prove a space lower bound of $$n^{\varOmega (k)}$$ for non-deterministic (syntactic) read-once branching programs (nrobps) on functions expressible as cnfs with treewidth at most k of their primal graphs. This lower bound rules out the possibility of fixed-parameter space complexity of nrobps parameterized by k. We use lower bound for nrobps to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the existing upper bound introduced by Beame et al. (Proceedings of the twenty-ninth conference on uncertainty in artificial intelligence, Bellevue, 2013) and thus proving the tightness of the latter.