Random strings make hard instances

We establish the truth of the "instance complexity conjecture" in the case of DEXT-complete sets w.r.t. polynomial time computations, and r.e. complete sets w.r.t. recursive computations. Specifically, we obtain for every DEXT-complete set A an exponentially dense subset C such that for every nondecreasing polynomial t(n)=/spl omega/(n log n), ic/sup t/(x:A)/spl ges/K/sup t/(x)-c holds for some constant c and all x/spl isin/C, where ic/sup t/ and K/sup t/ are the t-bounded instance complexity and Kolmogorov complexity measures, respectively. For r.e. complete sets A we obtain an infinite set C/spl sube/A~ such that ic/sup /spl infin(x:A)/spl ges/K/sup /spl infin(x)-c holds for some constant c and all x/spl isin/C. The proofs are based on the observation that Kolmogorov random strings are individually hard to recognize by bounded computations.<
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