Abstract
We consider the polynomial levelability with respect to approximation algorithms (PLAA). A setA isPLAA if given any approximation algorithmα forA and a polynomialp, there are another approximation algorithmβ forA and a polynomialq such that for infinitely many inputsx,α acceptsx but has running time greater thanp(|x|) andβ acceptsx within timeq(|x|). In this paper, an algorithmα is called an approximation algorithm forA if the symmetric differenceAΔL(α) is sparse, whereL(α) is the set of strings recognized byα. We prove that all naturalNP-complete sets arePLAA unlessP=NP and allEXP-complete sets arePLAA.
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