Gibbs measure =(G(V;E),{fu}vEv) f:[g]ego）→R≥o holant(()=Πf,(oE() o∈[glEv∈V Gibbs measure:Pr()= Πevf(oE(w) holant marginal probability:E[a)4 ACE Pr(a(e)=cA) self compute reduction FPTAS for Pr(o(e)=c|TA)±是 holant(S) in time poly(n)Gibbs Measure PWTIV\(￾) = ￾ ￾￾[q]E ￾ v￾V fv ￾ ￾ |E(v) ￾ ￾ = (G(V,E), {fv}v￾V ) Gibbs measure: marginal probability: fv : [q] LMO(v) ￾ R￾0 8Z(￾) = ￾ v￾V fv(￾|E(v)) PWTIV\ A ￾ E FPTAS for PWTIV\(￾) self￾reduction 8Z(￾(e) = c | ￾A) ￾A ￾ [q] A compute in time 8Z(￾(e) = c | ￾A) ± 1 n XWTa (n)