Inseparability and Strong Hypotheses for Disjoint NP Pairs

Abstract: This paper investigates the existence of inseparable disjoint pairs of NP languages and related strong hypotheses in computational complexity. Our main theorem says that, if NP does not have measure 0 in EXP, then there exist disjoint pairs of NP languages that are P-inseparable, in fact TIME(2^n^k)-inseparable. We also relate these conditions to strong hypotheses concerning randomness and genericity of disjoint pairs.