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REPORTS > KEYWORD > WEAK FUNCTIONAL PIGEONHOLE PRINCIPLE:
Reports tagged with Weak functional pigeonhole principle:
TR01-075 | 2nd November 2001
Alexander Razborov

#### Resolution Lower Bounds for the Weak Functional Pigeonhole Principle

We show that every resolution proof of the {\em functional} version
$FPHP^m_n$ of the pigeonhole principle (in which one pigeon may not split
between several holes) must have size $\exp\of{\Omega\of{\frac n{(\log m)^2}}}$. This implies an $\exp\of{\Omega(n^{1/3})}$ bound when the number
of pigeons $m$ is arbitrary.

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