Given a class F of functions, we define PCP of (r,F) as the union of the classes PCP [r,q] for all q belonging to F.
By definition of NP we have that NP is equal to PCP(0, poly), where poly is the set of polynomials.
But the PCP theorem states that instead NP is equal to PCP of log, where log is a set of logarithmic function and O(1), where O(1) is a set of constant function.
So this means that we can check problems in NP by using a logarithmic number of random bits and by querying a constant number of bits in the proof.
This is a very interesting result, whose prove is easy in one direction but very difficult in the other direction.
