Hausdor Reductions to Sparse Sets and toSets of High Information
نویسنده
چکیده
We investigate the complexity of sets that have a rich internal structure and at the same time are reducible to sets of either low or very high information content. In particular, we show that every length-decreasing or word-decreasing self-reducible set that reduces to some sparse set via a non-monotone variant of the Hausdorr reducibility is low for p 2. Measuring the information content of a set by the space-bounded Kol-mogorov complexity of its characteristic sequence, we further investigate the (non-uniform) complexity of sets A in EXPSPACE=poly that reduce to some set having very high information content. Speciically, we show that if the reducibility used has a certain property, called \reliability," then A in fact is reducible to a sparse set (under the same reducibil-ity). As a consequence of our results, the existence of hard sets (under \reliable" reducibilities) of very high information content is unlikely for various complexity classes as for example NP; PP, and PSPACE.
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