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.

翻译：我们通过证明复杂性类PWPP（多项式弱鸽巢原理）在黑盒设定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。此前已知PWPP对非自适应图灵归约封闭（Jeřábek 2016）。我们通过引入NESTED-COLLISION问题——定义在一对收缩函数上的自然碰撞查找问题——来证明这一黑盒分离性。我们表明，虽然该问题可通过两次对PWPP预言机的自适应调用来求解，但无法通过从经典PWPP完全问题COLLISION出发的有效黑盒非自适应归约来解决。