Every sequence X is quasi-polynomial-time reducible to a polynomial-time random R with n+o(n) oracle use, ρ⁻_poly(X) equals K_poly(X), and Kučera-Gács fails at finite-state level since reductions from normal sequences must yield convergent frequencies.
A complexity theoretic approach to randomness
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Resource bounded Ku\v{c}era-G\'{a}cs Theorems
Every sequence X is quasi-polynomial-time reducible to a polynomial-time random R with n+o(n) oracle use, ρ⁻_poly(X) equals K_poly(X), and Kučera-Gács fails at finite-state level since reductions from normal sequences must yield convergent frequencies.