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Electronic Colloquium on Computational Complexity

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Reports tagged with PPP:
TR22-089 | 18th June 2022
Ilario Bonacina, Neil Thapen

A separation of PLS from PPP

Recently it was shown that PLS is not contained in PPADS (ECCC report TR22-058). We show that this separation already implies that PLS is not contained in PPP. These separations are shown for the decision tree model of TFNP and imply similar separations in the type-2, relativized model.

Important note. ... more >>>

TR24-010 | 19th January 2024
Noah Fleming, Stefan Grosser, Toniann Pitassi, Robert Robere

Black-Box PPP is not Turing-Closed

The complexity class PPP contains all total search problems many-one reducible to the PIGEON problem, where we are given a succinct encoding of a function mapping n+1 pigeons to n holes, and must output two pigeons that collide in a hole. PPP is one of the “original five” syntactically-defined subclasses ... more >>>

TR24-018 | 28th January 2024
Huck Bennett, Surendra Ghentiyala, Noah Stephens-Davidowitz

The more the merrier! On the complexity of finding multicollisions, with connections to codes and lattices

We study the problem of finding multicollisions, that is, the total search problem in which the input is a function $\mathcal{C} : [A] \to [B]$ (represented as a circuit) and the goal is to find $L \leq \lceil A/B \rceil$ distinct elements $x_1,\ldots, x_L \in A$ such that $\mathcal{C}(x_1) = ... more >>>

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