Non-autoreducible Sets for NEXP.

We investigate autoreducibility properties of complete sets for NEXP under different polynomial-time reductions. Specifically, we show that under some polynomial-time reductions there are complete sets for NEXP that are not autoreducible. We show that settling the question whether every <=(dttp)-complete set for NEXP is <=(p)(NOR-tt) autoreducible either positively or negatively would lead to major results about the exponential time complexity classes.