Emergent Mind
Small circuits and dual weak PHP in the universal theory of p-time algorithms
(2004.11582)
Published Apr 24, 2020
in
math.LO
and
cs.CC
Abstract
We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending $n$ bits to $m \geq n2$ bits violates the dual weak pigeonhole principle: every string $y$ of length $m$ equals the value of the function for some $x$ of length $n$. The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size $nd$.
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