Structural Properties Of Nonautoreducible Sets

We investigate autoreducibility properties of complete sets for NEXP under different polynomial-time reductions. Specifically, we show under some polynomial-time reductions that there are complete sets for NEXP that are not autoreducible. We obtain the following main results:-For any positive integers s and k such that 2(s) - 1 > k, there is a <=(p)(s-T)-complete set for NEXP that is not <=(p)(k-tt)-autoreducible.-For every constant c > 1, there is a <=(p)(2-T)-complete set for NEXP that is not autoreducible under nonadaptive reductions that make no more than three queries, such that each of them has a length between n(1/c) and n(c), where n is input size.-For any positive integer k, there is a <=(p)(k-tt)-complete set for NEXP that is not autoreducible under <=(p)(k-tt)-reductions whose truth table is not a disjunction or a negated disjunction.Finally, we show that settling the question of whether every <=(p)(dtt)-complete set for NEXP is <=(p)(NOR-tt)-autoreducible either positively or negatively would lead to major results about the exponential time complexity classes.