On Algorithmic Statistics for Space-bounded Algorithms

Algorithmic statistics looks for models of observed data that are good in the following sense: a model is simple (i.e., has small Kolmogorov complexity) and captures all the algorithmically discoverable regularities in the data. However, this idea can not be used in practice as is because Kolmogorov complexity is not computable. In this paper we develop an algorithmic version of algorithmic statistics that uses space-bounded Kolmogorov complexity. We prove a space-bounded version of a basic result from “classical” algorithmic statistics, the connection between optimality and randomness deficiences. The main tool is the Nisan–Wigderson pseudo-random generator. An extended abstract of this paper was presented at the 12th International Computer Science Symposium in Russia (Milovanov 10).