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In this paper we prove a space lower bound of $n^{\Omega(k)}$ fornon-deterministic (syntactic) read-once branching programs ({\sc nrobp}s) onfunctions expressible as {\sc cnf}s with treewidth at most $k$ of their primalgraphs. This lower bound rules out the possibility of fixed-parameter spacecomplexity of {\sc nrobp}s parameterized by $k$.  We use lower bound for {\sc nrobp}s to obtain a quasi-polynomial separationbetween Free Binary Decision Diagrams and Decision Decomposable Negation NormalForms, essentially matching the existing upper bound introduced by Beame et al.and thus proving the tightness of the latter.

On the read-once property of branching programs and CNFs of bounded treewidth