The permanent, graph gadgets and counting solutions for certain types of planar formulas

Abstract

In this paper, we build on the idea of Valiant [13] and Ben-Dor/Halevi [3], that is, to count the number of satisfying solutions of a boolean formula via computing the permanent of a specially constructed matrix. We show that the Desnanot-Jacobi identity (DJi) prevents Valiant’s original approach to achieve a parsimonious reduction to the permanent over a… (More)

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18 Figures and Tables