A minimal pair of K-degrees

We construct a minimal pair of K-degrees. We do this by showing the existence of an unbounded nondecreasing function f which forces K-triviality in the sense that γ ∈ 2 ω is K-trivial if and only if for all n, K(γ | n) ≤ K(n) + f(n) + O(1).

[1]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[2]  Paul M. B. Vitányi,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 1993, Graduate Texts in Computer Science.

[3]  André Nies,et al.  Trivial Reals , 2002, CCA.

[4]  Rodney G. Downey,et al.  Randomness and reducibility , 2004, J. Comput. Syst. Sci..

[5]  Rodney G. Downey,et al.  The Kolmogorov complexity of random reals , 2004, Ann. Pure Appl. Log..

[6]  André Nies,et al.  Calibrating Randomness , 2006, Bull. Symb. Log..