A note on the number of N-bit strings with maximum complexity

Consider the number of n-bit strings that have exactly the maximum possible program-size complexity that an n-bit string can have. We show that this number is itself an n-bit string with nearly the maximum possible complexity. From this it follows that at least 2n-c n-bit strings have exactly the maximum complexity that it is possible for an n-bit string to have. © 1993.