Randomized Lower Bounds for Tarski Fixed Points in High Dimensions

The Knaster-Tarski theorem, also known as Tarski's theorem, guarantees that every monotone function defined on a complete lattice has a fixed point. We analyze the query complexity of finding such a fixed point on the \(k\)-dimensional grid of side length \(n\) under the \(\leq\) relation. Spec...

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Veröffentlicht in:	arXiv.org 2024-12
Hauptverfasser:	Brânzei, Simina, Phillips, Reed, Recker, Nicholas
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Boolean Complexity Dimensional analysis Fixed points (mathematics) Hypercubes Lower bounds Queries Theorems
Online-Zugang:	Volltext
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