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In this paper we study complexity of an extension of ordered binary decisiondiagrams (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$\Omega(n^{k/(8c-4)})$. Moreover, this lower bound holds if $c$-OBDD isnon-deterministic and semantic. Our second result uses the above lower bound toseparate the above model from sentential decision diagrams (SDDs). In order toobtain the lower bound, we use a structural graph parameter called matchingwidth. Our third result shows that matching width and pathwidth are linearlyrelated.

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