On Time-Bounded Incompressibility of Compressible Strings and Sequences
نویسندگان
چکیده
For every total recursive time bound t, a constant fraction of all compressible (low Kolmogorov complexity) strings is t-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length n is compressible to log n yet t-bounded incompressible below 1 4n − log n; and there are a countably infinite number of recursive infinite sequences of which every initial segment is similarly t-bounded incompressible. These results and their proofs are related to, but different from, Barzdins’s lemma.
منابع مشابه
Time-bounded incompressibility of compressible strings and sequences
For every total recursive time bound t, a constant fraction of all compressible (low Kolmogorov complexity) strings is t-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length n is compressible to log n yet t-bounded incompressible below 1 4n− log n; and there are countable infinitely many recursiv...
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