Understanding model counting for β-acyclic CNF-formulas
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We extend the knowledge about so-called structural restrictions of #SAT by giving a polynomial time algorithm for β-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 β-acyclic #SAT.
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