Dan Boneh

To present the application of the XOR Theorem to learning theory we rst give the following two de nitions. Let F be a class of boolean functions and let > 0. A strong learning algorithm for F over the uniform distribution queries the function f : f0; 1gn ! f0; 1g and outputs, with probability at least 1 , a circuit C such that Pr[f(x) 6= C(x)] < 1 nO(1) where Pr is the uniform distribution. The algorithm is said to be polynomial if it is polynomial in n; ln 1 .