Black-Box PWPP Is Not Turing-Closed

Pavel Hubáček

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arXiv · 2602.23809

Black-Box PWPP Is Not Turing-Closed

Pavel Hubáček

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Abstract

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 (Je\v{r}\'abek 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.

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Pavel Hubáček. 2026-02-27. Black-Box PWPP Is Not Turing-Closed. https://arxiv.org/abs/2602.23809

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