On The Expressive Power Of Non-Linear Merge-And-Shrink Representations

We prove that general merge-and-shrink representations are strictly more powerful than linear ones by showing that there exist problem families that can be represented compactly with general merge-and-shrink representations but not with linear ones. We also give a precise bound that quantifies the necessary blowup incurred by conversions from general merge-and-shrink representations to linear representations or BDDs/ADDs. Our theoretical results suggest an untapped potential for non-linear merging strategies and for the use of non-linear merge-and-shrink-like representations within symbolic search.