Succinct representation random strings, and complexity classes

A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence of strings which are random with respect to one measure but not to another can show the relationship between the corresponding complexity classes. The basic hierarchy theorems given allow different and possibly more powerful approaches to these problems.