Inseparability and Strong Hypotheses for Disjoint NP Pairs

TL;DR

This paper explores the existence of inseparable disjoint NP language pairs and links their properties to strong hypotheses about randomness and genericity in computational complexity.

Contribution

It establishes that if NP lacks measure zero in EXP, then P-inseparable disjoint NP pairs exist, connecting complexity theory with randomness hypotheses.

Findings

Existence of P-inseparable disjoint NP pairs under certain conditions

Relation between inseparability and measure hypotheses in complexity classes

Connections to randomness and genericity hypotheses in NP

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.