Some lower bounds in parameterized ${\rm AC}^0$

Yijia Chen; Joerg Flum

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arXiv · 1606.08014

Some lower bounds in parameterized ${\rm AC}^0$

Yijia Chen·Joerg Flum

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Abstract

We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical ${\rm AC}^0$. Among others, we derive such a lower bound for all fpt-approximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the first lower bound, we prove a strong ${\rm AC}^0$ version of the planted clique conjecture: ${\rm AC}^0$-circuits asymptotically almost surely can not distinguish between a random graph and this graph with a randomly planted clique of any size $\le n^\xi$ (where $0 \le \xi < 1$).

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Yijia Chen, Joerg Flum. 2016-06-26. Some lower bounds in parameterized ${\rm AC}^0$. https://arxiv.org/abs/1606.08014

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