On oblivious branching programs with bounded repetition that cannot efficiently compute CNFs of bounded treewidth

In this paper we study complexity of an extension of ordered binary decision diagrams (OBDDs) called $c$-OBDDs on CNFs of bounded (primal graph) treewidth. In particular, we show that for each $k$ there is a class of CNFs of treewidth $k \geq 3$ for which the equivalent $c$-OBDDs are of size $Ω(n^{k/(8c-4)})$. Moreover, this lower bound holds if $c$-OBDD is non-deterministic and semantic. Our second result uses the above lower bound to separate the above model from sentential decision diagrams (SDDs). In order to obtain the lower bound, we use a structural graph parameter called matching width. Our third result shows that matching width and pathwidth are linearly related.