LLL condition::3:A→(0，+∞) S∈A:as±Pr[n4esA, HA∈A:Pr[A]≤ MA s合 T+(A) ∑Ia Indep.IcSA∈l Recursive bounds: S∈A,BeS: 4s\(B)4s+Pr(B)qs\r+(B) VS∈A,BtS: USU(B)2 us +Pr(B)usur+(B) 4ua=∑+∑Πa I∈S Indep.IsSA∈l BEIndep.IESUB AEI B∈I∈SU{B} Indep.I∈SU{B} ∀𝑆 ⊆ 𝒜: 𝑞෬𝑆 ≜ Pr[⋂𝐴∈𝑆𝐴ҧ], 𝜇𝑆 ≜ ෍ 𝐼𝑛𝑑𝑒𝑝. 𝐼⊆𝑆 ෑ 𝐴∈𝐼 𝜇𝐴 Recursive bounds: 𝑞෬𝑆∖ 𝐵 ≤ 𝑞෬𝑆 + Pr 𝐵 𝑞෬𝑆∖Γ + 𝐵 𝜇𝑆∪{𝐵} ≥ 𝜇𝑆 + Pr(𝐵) 𝜇𝑆∪Γ + ∀𝑆 ⊆ 𝒜 (𝐵) , 𝐵 ∉ 𝑆: 𝜇𝑆∪{𝐵} = ෍ 𝐼𝑛𝑑𝑒𝑝. 𝐼⊆𝑆 ෑ 𝐴∈𝐼 𝜇𝐴 + ෍ 𝐵∈𝐼𝑛𝑑𝑒𝑝. 𝐼⊆𝑆∪𝐵 ෑ 𝐴∈𝐼 𝜇𝐴 LLL condition: ∃𝜇: 𝒜 → (0, +∞) ∀𝐴 ∈ 𝒜: Pr[𝐴] ≤ 𝜇𝐴 𝜇Γ+(𝐴) ∀𝑆 ⊆ 𝒜, 𝐵 ∈ 𝑆: 𝐵 ∈ 𝐼 ⊆ 𝑆 ∪ 𝐵 𝐼 ⊆ 𝑆 𝐼𝑛𝑑𝑒𝑝. 𝐼 ⊆ 𝑆 ∪ 𝐵