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 ≥ 3 there is a class of CNFs of treewidth k for which the equivalent c-OBDDs are of size Ω(nk/(8c−4)). Moreover, this lower bound holds if c-OBDDs are 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.
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