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 ≤ s-T p -complete set for NEXP that is not ≤ k-tt p -autoreducible. —For every constant c > 1, there is a ≤ 2-T p -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 ≤ k-tt p -complete set for NEXP that is not autoreducible under ≤ k-tt p -reductions whose truth table is not a disjunction or a negated disjunction. Finally, we show that settling the question of whether every ≤ dtt p -complete set for NEXP is ≤ NOR-tt p -autoreducible either positively or negatively would lead to major results about the exponential time complexity classes.