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Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity
[article]

2022
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arXiv
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pre-print

The classical coding theorem in Kolmogorov complexity states that if an n-bit string x is sampled with probability δ by an algorithm with prefix-free domain then K(x) ≤log(1/δ) + O(1). In a recent work, Lu and Oliveira [LO21] established an unconditional time-bounded version of this result, by showing that if x can be efficiently sampled with probability δ then rKt(x) = O(log(1/δ)) + O(log n), where rKt denotes the randomized analogue of Levin's Kt complexity. Unfortunately, this result is

arXiv:2204.08312v1
fatcat:g5y7win7wndgdguem6t5xxzqrq