Spin System Aa Ab Ae:[g]×[g→R≥o Af Fv:[gl→R≥0 F Ae F partition function:count the of solutions to an CSP Ⅱe(ru,)Π，(c》 ∈[qy e=uw∈E w∈V enumerate all binary constraints unary constraints configurations 17 1 coloring:A= F .. 1Spin System Z = X x2[q]V Y e=uv2E Ae(xu, xv) Y v2V Fv(xv) Aa Ab Ac Ad Ae Af Fw Fu Fv Fy Fx enumerate all configurations binary constraints unary constraints A = 2 6 6 6 4 0 0 ... 0 3 7 7 7 5 1 1 F = 2 6 6 6 4 1 1 . . . 1 3 7 7 7 5 Ae : [q] ⇥ [q] ! R￾0 Fv : [q] ! R￾0 coloring: partition function: count the # of solutions to an CSP