Understanding model counting for β-acyclic CNF-formulas

Abstract

We extend the knowledge about so-called structural restrictions of \#SAT by giving a polynomial time algorithm for -acyclic \#SAT. In contrast to previous algorithms in the area, our algorithm does not proceed by dynamic programming but works along an elimination order, solving a weighted version of constraint satisfaction. Moreover, we give evidence that this deviation from more standard algorithm is not a coincidence, but that there is likely no dynamic programming algorithm of the usual style for -acyclic \#SAT.

Tasks

Reproductions