DNF counting

Rare events

• if p small, huge sample size
• importance sampling biases samples toward event.

Complexity:

• $\SP$-complete.
• PRAS, FPRAS

Coverage algorithm

• given A_i $\subseteq$V, count $\cup$A_i
• problem: random a $\in$V too rarely satisfies
• work in $\uplus$A_i
• size known
• can sample uniformly
• dense subset of right size
• assignment a, satisfies s_a clauses.
• $\sum_{a}^{}$(s_a/n)(1/s_a)
• prob. OK at least 1/m, so m trials suff.
• unbiased estimator