  We study the polynomial-time autoreducibility of NP-complete sets and obtain
separations under strong hypotheses for NP. Assuming there is a p-generic set
in NP, we show the following:
  - For every $k \geq 2$, there is a $k$-T-complete set for NP that is $k$-T
autoreducible, but is not $k$-tt autoreducible or $(k-1)$-T autoreducible.
  - For every $k \geq 3$, there is a $k$-tt-complete set for NP that is $k$-tt
autoreducible, but is not $(k-1)$-tt autoreducible or $(k-2)$-T autoreducible.
  - There is a tt-complete set for NP that is tt-autoreducible, but is not
btt-autoreducible.
  Under the stronger assumption that there is a p-generic set in NP $\cap$
coNP, we show:
  - For every $k \geq 2$, there is a $k$-tt-complete set for NP that is $k$-tt
autoreducible, but is not $(k-1)$-T autoreducible.
  Our proofs are based on constructions from separating NP-completeness
notions. For example, the construction of a 2-T-complete set for NP that is not
2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility.
