We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations.

翻译：我们研究了TFNP中问题之间的确定性与随机化黑盒归约之间的关系。我们的主要贡献是一种通用技术，该技术建立了从特定TFNP问题到任意TFNP问题的这些归约类型之间的等价性。特别地，我们证明这种等价性对于从PPP、PPAD、PPA和$t$-PPP中的完备问题出发的归约成立。进而，这强化了所有已知的源于这些类的黑盒分离结果，将其提升为随机化分离。