an:06382102
Zbl 1317.68131
Rumyantsev, Andrei; Shen, Alexander
Probabilistic constructions of computable objects and a computable version of Lovász local lemma
EN
Fundam. Inform. 132, No. 1, 1-14 (2014).
0169-2968 1875-8681
2014
j
68Q87 03D32 05D40 68Q30
Summary: 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 [the first author, ``Infinite computable version of Lovász local lemma'', Preprint, \url{arXiv:1012.0557}], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.