Almost Every Set in Exponential Time is P-Bi-Immune (1994)
| Venue: | Theoretical Computer Science |
| Citations: | 51 - 5 self |
BibTeX
@ARTICLE{Mayordomo94almostevery,
author = {Elvira Mayordomo},
title = {Almost Every Set in Exponential Time is P-Bi-Immune},
journal = {Theoretical Computer Science},
year = {1994},
volume = {136},
pages = {392--400}
}
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Abstract
. A set A is P-bi-immune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of P-bi-immune languages in linearexponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies that `almost' every language in E is P-bi-immune, that is to say, almost every set recognizable in linear exponential time has no algorithm that recognizes it and works in polynomial time on an infinite number of instances. A bit further, we show that every p-random (pseudo-random) language is E-bi-immune. Regarding the existence of P-bi-immune sets in NP, we show that if NP does not have measure 0 in E, then NP contains a P-bi-immune set. Another consequence is that the class of p m -complete languages for E has measure 0 in E. In contrast, it is shown that in E, and even in REC, the class of P-bi-immune languages lacks the property of Baire (the Baire category analogue of Lebesgue measurability). * This work was supported by a Spani...
