Universal distributions and time-bounded kolmogorov complexity

Abstract

The equivalence of the universal distribution, the a priori probability and the negative exponential of Kolmogorov complexity is a well known result. The natural analogs of Kolmogorov complexity and of a priori probability in the time-bounded setting are not eficiently computable under reasonable assumptions. In contrast, it is known that for every polynomial p, distributions universal for the class of p-time computable distributions can be computed in polynomial time. We show that in the time-bounded setting the universal distribution gives rise to sensible notions of Kolmogorov complexity and of a priori probability.