Abstract
We consider two setsA andB to be close to each other if the census of their symmetric difference,A ▵B, is a slowly increasing function (e.g. a polynomial.) The classes of sets which are polynomially close to some set in a complexity classC (likeP) are studied and characterized. We investigate the question whether complete sets forNP or EXPTIME can be polynomially close to a set inP. Some of the obtained results strengthen or generalize results by Yesha [24], e.g. it is shown that no EXPTIME-hard set can be polynomially close to any set inP.
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