Abstract

An oracle A is k-cheatable if there is a polynomial-time algorithm to determine the answers to 2 k parallel queries to A from the answers to only k queries to some other oracle B. It is known that 1-cheatable sets cannot be bi-immune for P. In contrast, we construct 2-cheatable sets that are bi-immune for arbitrary time complexity classes. In addition, for each k, we construct a set that is (k + 1)-cheatable, but not k-cheatable; we show that this separation does not hold with biimmunity. We show that if a recursive set A is bi-immune for P then there exists an infinite 1-cheatable set that is polynomial-time mreducible to A. Consequently if NP contains a set that is bi-immune for P then NP contains a set that is not polynomial-time Turingequivalent to a self-reducible set. 1. Introduction Complexity theory deals with how hard problems are. Time, space, and alternation have served as measures of difficulty. Recently, researchers have Research supported by a Fannie and John Hertz ...

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