Complexity classes and sparse oracles

Abstract

The authors obtain positive relativization results. In particular, the goal is to prove statements of the kind: 'Given two complexity classes C/sub 1/ and C/sub 2/, C/sub 1/=C/sub 2/ if and only if for every sparse set S, C/sub 1//sup S/=C/sub 2//sup S/.' The authors derive a sufficient condition to obtain such results and, as an application, they prove a general theorem from which, as far as they know, all of the results obtained previously along with new ones can be immediately derived.<>