Kolmogorov complexity, pseudorandom generators and statistical models testing

0411049 - UTIA-B 20030036 RIV CZ eng J - Journal Article
Šindelář, Jan - Boček, Pavel
Kolmogorov complexity, pseudorandom generators and statistical models testing.
Kybernetika. Roč. 38, č. 6 (2002), s. 747-759. ISSN 0023-5954
R&D Projects: GA ČR GA102/99/1564
Institutional research plan: CEZ:AV0Z1075907
Keywords : Kolmogorov complexity * pseudorandom generators * statistical models testing
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.341, year: 2002

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.
Permanent Link: http://hdl.handle.net/11104/0131136