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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机译：在DEXT完备集w.r.t.的情况下，我们建立了“实例复杂性猜想”的真相。多项式时间计算和r.e.全套w.r.t.递归计算。具体来说，我们为每个DEXT完全集A获得一个指数密集子集C，这样对于每个非递减多项式t（n）= / spl omega /（n log n），ic / sup t /（x：A）/ splges / K / sup t /（x）-c对于某些常数c和所有x / spl isin / C都成立，其中ic / sup t /和K / sup t /分别是t边界实例复杂度和Kolmogorov复杂度度量。对于r.e.完整的集合A我们获得一个无限的集合C / spl sube / A〜，使得ic / sup / spl infin（x：A）/ spl ges / K / sup / spl infin（x）-c对于某些常数c均成立x / spl isin / C。证明是基于观察到的事实，即Kolmogorov随机字符串很难通过有限的计算来单独识别。
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