AbstractWe 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 $${k \geq 2}$$k≥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 $${k \geq 3}$$k≥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 $${k \geq 2}$$k≥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.

中文翻译：

---

强假设下 NP 完全集的自约性

摘要 我们研究了 NP 完备集的多项式时间自还原性，并在 NP 的强假设下获得了分离。假设在 NP 中有一个 p-generic 集，我们显示如下： ◦对于每一个 $${k \geq 2}$$k≥2，对于 NP 有一个 kT-完全集是 kT-autoreducible，但是不是 k-tt-autoreducible 或 (k − 1)-T-autoreducible。◦对于每一个 $${k \geq 3}$$k≥3，对于 NP 有一个 k-tt-完全集是 k-tt -autoreducible，但不是 (k − 1)-tt-autoreducible 或 (k − 2)-T-autoreducible。◦NP 的 tt-complete 集是 tt-autoreducible，但不是 btt-autoreducible。在 NP $${\cap}$$∩ coNP 中存在 p-泛型集的更强假设下，我们证明： ◦对于每一个 $${k \geq 2}$$k≥2，有一个 k- NP 的 tt-完全集是 k-tt-autoreducible，但不是 (k − 1)-T-autoreducible。我们的证明基于分离 NP 完整性概念的构造。例如，为非 2-tt-完全的 NP 构建 2-T-完全集也将 2-T-自还原性与 2-tt-自还原性分开。