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Algebra Logika, 2018, Volume 57, Number 4, Pages 448–455 (Mi al858)  

Generic amplification of recursively enumerable sets

A. N. Rybalov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia

Abstract: Generic amplification is a method that allows algebraically undecidable problems to generate problems undecidable for almost all inputs. It is proved that every simple negligible set is undecidable for almost all inputs, but it cannot be obtained via amplification from any undecidable set. On the other hand, it is shown that every recursively enumerable set with nonzero asymptotic density can be obtained via amplification from a set of natural numbers.

Keywords: algorithmically undecidable problem, generic amplification, undecidable set, simple negligible set, recursively enumerable set.

Funding Agency Grant Number
Russian Science Foundation 18-71-10028
Supported by Russian Science Foundation, project No. 18-71-10028.


DOI: https://doi.org/10.17377/alglog.2018.57.403

Full text: PDF file (139 kB)
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English version:
Algebra and Logic, 2018, 57:4, 289–294

Bibliographic databases:

UDC: 510.5
Received: 19.04.2017
Revised: 15.04.2018

Citation: A. N. Rybalov, “Generic amplification of recursively enumerable sets”, Algebra Logika, 57:4 (2018), 448–455; Algebra and Logic, 57:4 (2018), 289–294

Citation in format AMSBIB
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\pages 448--455
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