Kolmogorov complexity, pseudorandom generators and statistical models testing

Journal Article

Šindelář Jan, Boček Pavel

serial: Kybernetika vol.38, 6 (2002), p. 747-759

research: CEZ:AV0Z1075907

project(s): GA102/99/1564, GA ČR

keywords: Kolmogorov complexity, pseudorandom generators, statistical models testing

abstract (eng):

An attempt to formalize heuristic concepts like strings (sequence resp.) "typical" for a probability measure is stated in the paper. Both generating and testing of such strings is considered. Kolmogorov complexity theory is used as a tool. It is shown that no pseudorandom generator can produce long "typical" strings. The time complexity of pseudorandom generators with oracles capable to recognize "typical" strings is shown to be at least exponential with respect to the length of the output.

Cosati: 12B

RIV: BB