Year: 2016
Type: preprint
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 $\le n^ξ$ (where $0 \le ξ< 1$).
Source: arXiv (Cornell University)
Authors: Chen, Yijia, Flum, Joerg
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2464394875