Small circuits and dual weak PHP in the universal theory of p-time algorithms

Jan Krajicek

doi:10.1145/3446207

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arXiv · 2004.11582

Small circuits and dual weak PHP in the universal theory of p-time algorithms

Jan Krajicek

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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 $m \geq n^2$ 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 $n^d$.

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BibTeX RIS

Jan Krajicek. 2020-04-24. Small circuits and dual weak PHP in the universal theory of p-time algorithms. https://doi.org/10.1145/3446207

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