Computational complexity and Gödel's incompleteness theorem

@inproceedings{Chaitin1971ComputationalCA,
  title={Computational complexity and G{\"o}del's incompleteness theorem},
  author={Gregory J. Chaitin},
  booktitle={SIGA},
  year={1971}
}
Given any simply consistent formal theory F of the state complexity L(S) of finite binary sequences S as computed by 3-tape-symbol Turing machines, there exists a natural number L(F) such that L(S) > n is provable in F only if n < L(F). On the other hand, almost all finite binary sequences S satisfy L(S) < L(F). The proof resembles Berry's paradox, not the Epimenides nor Richard paradoxes.