2026-08-19T10:43:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6442 2024-03-06T10:38:17Z ddc:004 open_access

Some Lower Bounds in Parameterized AC^0 Chen, Yijia Flum, Jörg parameterized AC^0 lower bound clique halting problem We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical 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 AC^0 version of the planted clique conjecture: AC^0-circuits asymptotically almost surely can not distinguish between a random graph and this graph with a randomly planted clique of any size <= n^xi (where 0 <= xi < 1). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yijia Chen and Jörg Flum 2016 Is Part Of LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2016.27 urn:nbn:de:0030-drops-64423 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.27 eng https://creativecommons.org/licenses/by/3.0/legalcode