Holant problem:Holant(9,F) graph family function family mptR-G,e）wm{食 output:holant()=>f(()) o∈[g]Ev∈V spin system /graph homomorphism(G.H.): F={f:[ga→C,d≤2}U{=} ●S,#VC .#q-colorings,#H-colorings .hardcore/lsing/Potts models,MRF G=(V,目 spin model holantHolant problem: PWTIV\(￾) = ￾ ￾￾[q]E ￾ v￾V fv ￾ ￾ |E(v) ￾ ￾ = (G(V,E), {fv}v￾V ) 0WTIV\(G, F) graph family function family input: output: ￾ G ￾ G fv ￾ F with F = {f : [q] d ￾ C, d ￾ 2} ￾ {=} spin system / graph homomorphism (G.H.): • #IS, #VC • #q-colorings, #H-colorings • hardcore/Ising/Potts models, MRF f G=(V,E) V E = = = = f f f f f spin model holant