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 nΩ(k), and - there are CNF formulas of size n and incidence neighborhood diversity k whose smallest DNNF-encoding has size nΩ(√k). These results complement recent upper bounds for compiling CNF into DNNF and strengthen-quantitatively and qualitatively-known conditional lower bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth.