A note on approximate inclusion-exclusion

Let Ai, i = l,…,n, be a sequence of sets, and for S⊂-[n] set as := ¦∩iϵSAi¦. Kahn, Linial and Samorodnitsky have recently shown that if it is known that u := ¦∪ni=1 Ai¦ < 2n−1 then u can be determined uniquely from a knowledge of the values of as for all S ≠ [n]. Since their proof was existential they posed the question of finding an adaptive procedure for determining u. Here we present such an algorithm.