Eyal Shlomo Shimony

Let A_i, i = l, . . . , n, be a sequence of sets, and for S ⊆[n] set as := | ∩_i∈s A_i |. Kahn, Linial and Samorodnitsky have recently shown that if it is known that u := | ∪_i=l ⁿ, A_i | < 2^n-l then u can be determined uniquely from a knowledge of the values of a_s 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.