Homogeneous measures and polynomial time invariants

Abstract

The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completeness results are so measure-independent and could lead to their generalization to this wider and more invariant class of measures. It also demonstrates a sharp difference between recently discovered pseudorandom strings and the objects known before.