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\r\n\r\n- there are CNF formulas of size n and modular incidence treewidth k whose smallest DNNF-encoding has size n^?(k), and\r\n\r\n- there are CNF formulas of size n and incidence neighborhood diversity k whose smallest DNNF-encoding has size n^?(?k).\r\n\r\nThese 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.