Probabilistic Constructions of Computable Objects and a Computable Version of Lov\'asz Local Lemma
Discrete Mathematics
2013-10-29 v2 Data Structures and Algorithms
Abstract
A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lov\'asz local lemma. (A survey of Moser-Tardos proof is included to make the paper self-contained.)
Cite
@article{arxiv.1305.1535,
title = {Probabilistic Constructions of Computable Objects and a Computable Version of Lov\'asz Local Lemma},
author = {Andrei Rumyantsev and Alexander Shen},
journal= {arXiv preprint arXiv:1305.1535},
year = {2013}
}
Comments
10 pages. arXiv admin note: substantial text overlap with arXiv:1012.0557