Superlinear lower bounds based on ETH
Abstract
We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in essentially-linear time unless the exponential time hypothesis (ETH) is false and k-Clique is decidable in essentially-linear time in terms of the graph's size for all fixed k. Such conditional lower bounds have previously only been demonstrated relative to the strong exponential time hypothesis (SETH). Our results therefore offer significant progress towards proving unconditional superlinear time complexity lower bounds for natural problems in polynomial time.
Citation
Salamon , A Z & Wehar , M 2022 , Superlinear lower bounds based on ETH . in P Berenbrink & B Monmege (eds) , Symposium on Theoretical Aspects of Computer Science (STACS 2022) . , 14 , Leibniz International Proceedings in Informatics , Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH , The 39th International Symposium on Theoretical Aspects of Computer Science , 15/03/22 . https://doi.org/10.4230/LIPIcs.STACS.2022.55 conference
Publication
Symposium on Theoretical Aspects of Computer Science (STACS 2022)
ISSN
1868-8969Type
Conference item
Description
Andras Z. Salamon acknowledges support from EPSRC grants EP/P015638/1 and EP/V027182/1.Collections
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