Kolmogorov complexity cores

Authors:
André Souto
Affiliations:
Universidade do Porto and Instituto de Telecomunicações
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

We study the relationship between complexity cores of a language and the descriptional complexity of the characteristic sequence of the language based on Kolmogorov complexity. We prove that a recursive set A has a complexity core if for all constants c, the computational depth (the difference between time-bounded and unbounded Kolmogorov complexities) of the characteristic sequence of A up to length n is larger than c infinitely often. We also show that if a language has a complexity core of exponential density, then it cannot be accepted in average polynomial time, when the strings are distributed according to a time bounded version of the universal distribution.