黑盒 PWPP 不是图灵封闭的
Black-Box PWPP Is Not Turing-Closed
AI总结：
通过引入嵌套碰撞问题，证明了在自适应查询下 PWPP 类具有更强的能力，黑盒设置下 PWPP 对自适应图灵归约不封闭。
摘要：
我们通过证明复杂度类 PWPP（多项式弱鸽巢原理）在黑盒设置下对自适应图灵归约不封闭，确立了自适应碰撞查找查询严格强于非自适应查询。此前，PWPP 已知对非自适应图灵归约封闭（Jeřábek 2016）。我们通过引入 NESTED-COLLISION 问题来展示这种黑盒分离，该问题是在一对收缩函数上定义的自然碰撞查找问题。我们证明，虽然该问题可以通过对 PWPP 预言机的两次自适应调用来解决，但它无法通过高效的、对典型 PWPP 完全问题 COLLISION 的黑盒非自适应归约来解决。
英文摘要：
We establish that adaptive collision-finding queries are strictly more powerful than non-adaptive ones by proving that the complexity class PWPP (Polynomial Weak Pigeonhole Principle) is not closed under adaptive Turing reductions in the black-box setting. Previously, PWPP was known to be closed under non-adaptive Turing reductions (Jeřábek 2016). We demonstrate this black-box separation by introducing the NESTED-COLLISION problem, a natural collision-finding problem defined on a pair of shrinking functions. We show that while this problem is solvable via two adaptive calls to a PWPP oracle, it cannot be solved via an efficient black-box non-adaptive reduction to the canonical PWPP-complete problem COLLISION.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
