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.
Cite
@article{arxiv.2602.23809,
title = {Black-Box PWPP Is Not Turing-Closed},
author = {Pavel Hubáček},
journal= {arXiv preprint arXiv:2602.23809},
year = {2026}
}
Comments
This version weakens the main theorem from fully black-box reductions to the decision-tree setting. This change avoids a gap in the earlier formalism while preserving the overall proof strategy