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.
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The quasilinear isomorphism challenge
Regan, Kenneth W.; Wang, Jie
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, Volume 25 (3)
Association for Computing Machinery – Sep 1, 1994
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