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

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## 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.

## Keywords

Read-once branching programs CNFs Bounded treewidth Parameterized complexity Space complexity Lower bounds## References

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