Kolmogorov Characterizations of Complexity Classes

Abstract This paper completely characterizes the Θ k p levels of the polynomial hierarchy in terms of Kolmogorov complexity. From the characterization, it follows that the Θ k p and Δ k p levels of the polynomial hierarchy are equal if and only if every Δ k p language is accepted by some Δ k p machine whose pronouncements (query answers) are Kolmogorov simple. Analogous results are obtained for the exponential hierarchy.

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