eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-03-10
29:1
29:16
10.4230/LIPIcs.STACS.2021.29
article
A Faster Algorithm for Finding Tarski Fixed Points
Fearnley, John
1
Savani, Rahul
1
https://orcid.org/0000-0003-1262-7831
Department of Computer Science, University of Liverpool, UK
Dang et al. have given an algorithm that can find a Tarski fixed point in a k-dimensional lattice of width n using O(log^k n) queries [Chuangyin Dang et al., 2020]. Multiple authors have conjectured that this algorithm is optimal [Chuangyin Dang et al., 2020; Kousha Etessami et al., 2020], and indeed this has been proven for two-dimensional instances [Kousha Etessami et al., 2020]. We show that these conjectures are false in dimension three or higher by giving an O(log² n) query algorithm for the three-dimensional Tarski problem, which generalises to give an O(log^{k-1} n) query algorithm for the k-dimensional problem when k ≥ 3.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol187-stacs2021/LIPIcs.STACS.2021.29/LIPIcs.STACS.2021.29.pdf
query complexity
Tarski fixed points
total function problem