Abstract
The isomorphism conjecture is investigated for exponential-time and other complexity classes. If one-way functions exist, then we show that there are one-way functions such that A ≅ pf ( A), where A is a standard complete set for NP or E or NE. If one-way functions exist, we also show that there are k-completely creative sets in NP with one-way productive functions but which are p-isomorphic to standard complete sets. We then present a type of one-way functions whose existence is equivalent to the failure of the isomorphism conjecture for E. Finally, we show that the isomorphism conjecture holds for E (NE) if and only if it holds for EXP (NEXP).
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