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

In this paper we prove a space lower bound of n^ (k) for non-deterministic (syntactic) read-once branching programs ( nrobp s) on functions expressible as cnf s with treewidth at most k of their primal graphs. This lower bound rules out the possibility of fixed-parameter space complexity of nrobp s parameterized by k . We use lower bound for nrobp s 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.