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The complexity of Tarski’s fixed point theorem
- Source :
-
Theoretical Computer Science . Jul2008, Vol. 401 Issue 1-3, p228-235. 8p. - Publication Year :
- 2008
-
Abstract
- Abstract: Tarski’s fixed point theorem guarantees the existence of a fixed point of an order-preserving function defined on a nonempty complete lattice [B. Knaster, Un théorème sur les fonctions d’ensembles, Annales de la Société Polonaise de Mathématique 6 (1928) 133–134; A. Tarski, A lattice theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics 5 (1955) 285–309]. In this paper, we investigate several algorithmic and complexity-theoretic topics regarding Tarski’s fixed point theorem. In particular, we design an algorithm that finds a fixed point of when it is given as input and as an oracle. Our algorithm makes queries to when is a total order on . We also prove that when both and are given as oracles, any deterministic or randomized algorithm for finding a fixed point of makes an expected queries for some and . [Copyright &y& Elsevier]
- Subjects :
- *ALGORITHMS
*ALGEBRA
*FOUNDATIONS of arithmetic
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 401
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 32736518
- Full Text :
- https://doi.org/10.1016/j.tcs.2008.05.005