The quasilinear isomorphism challenge

Abstract

We show that all the basic facts about the Berman-Hartmanis Isomorphism Conjecture carry over from polynomial to quasilinear time bounds. However, we show that the connection between unique-accepting NTMs and one-way functions, which underlies much subsequent work on the B-H conjecture, breaks down for quasilinear time under relativizations. Hence we have a whole new ballgame, on a tighter playing field.