Sampling and Learning for Boolean Function

There, we laid out framework of discussions and proved some basic yet important results, such as: with sufficient data, universal learning machine can be achieved. The core of universal learning machine is X-form, which turns out to be a form of boolean function. We showed that the learning is actually equivalent to dynamics of X-form inside a learning machine. Thus, in order to study universal learning machine well, we need to study thoroughly X-form and the motion of X-form under driven of data. Since the work of [2, 4, 5], we have constantly pursued the effective learning dynamics, and tried to understand X-form, and more generally, boolean function and boolean circuit.