@MISC{Ogihara98gradedself-reducibility, author = {Mitsunori Ogihara and Kenneth W. Regan and Seinosuke Toda}, title = {Graded Self-Reducibility}, year = {1998} }

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Abstract

We introduce two special kinds of self-reducible sets that we call time-graded and spacegraded languages. Attaching time and space bounds to them yields a uniform, quantitative definition of resource-bounded self-reducibility that applies to all languages. We apply this to study the relationship between NSPACE[s(n)] and DSPACE[s(n) 2 ], emphasizing the case s(n) = O(log n). We show that the class of logspace-graded languages, which is contained in DSPACE[log 2 n], contains not only NL and uniform NC 2 , but also a class of Aux-PDA languages that is not known to be a subclass of P. We also prove that many-one space-graded classes are many-one equivalent to the special case in which the self-reduction makes one query to a string of strictly shorter length. For this latter idea of "instance contraction," we note that some NL-complete problems admit n-to-n=2 contraction in logspace, and prove that some NC 1 -complete problems are n-to-n=2 contractible by finite automata that invo...