For many pseudo-random generators, it is known what their period is. For most of those, it is known that they reach all possible states. For cryptographic qual

For many pseudo-random generators, it is known what their period is. For most of those, it is known that they reach all possible states. For cryptographic quality random generators, I am not sure how much is known. In any case, the question is a simple one, though answering it can be difficult in some cases.