Non-Uniform Reductions

We study properties of non-uniform reductions and related completeness notions. We strengthen several results of Hitchcock and Pavan (ICALP (1), Lecture Notes in Computer Science, vol. 4051, pp. 465–476, Springer, 2006) and give a trade-off between the amount of advice needed for a reduction and its honesty on NEXP. We construct an oracle relative to which this trade-off is optimal. We show, in a more systematic study of non-uniform reductions, among other things that non-uniformity can be removed at the cost of more queries. In line with Post’s program for complexity theory (Buhrman and Torenvliet in Bulletin of the EATCS 85, pp. 41–51, 2005) we connect such ‘uniformization’ properties to the separation of complexity classes.

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