PWPP ⊆ PPP

Inclusion · folklore

Statement

Weak Pigeon reduces to Pigeon, so PWPP $\subseteq$ PPP — folklore.

Sketch

Given $C:\{0,1{\}}^n\to \{0,1{\}}^{n-1}$, let $C^{\prime }(x):=1\Vert C(x)$, a map $\{0,1{\}}^n\to \{0,1{\}}^n$ that never outputs $0^n$; every Pigeon solution for $C^{\prime }$ is a collision of $C^{\prime }$, hence of $C$.