Parameterized Compilation Lower Bounds for Restricted CNF-formulas

Abstract

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures. In particular, we show that - there are CNF formulas of size n and modular incidence treewidth k whose smallest DNNF-encoding has size n^(k), and - there are CNF formulas of size n and incidence neighborhood diversity k whose smallest DNNF-encoding has size n^(k). These results complement recent upper bounds for compiling CNF into DNNF and strengthen---quantitatively and qualitatively---known conditional low\-er bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth.

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