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.
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Souto, A. (2010). Kolmogorov Complexity Cores. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_42
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DOI: https://doi.org/10.1007/978-3-642-13962-8_42
Publisher Name: Springer, Berlin, Heidelberg
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