CT-1994-09: Ambos-Spies, Klaus and Terwijn, Sebastiaan A. and Xizhong, Zheng (1994) Resource Bounded Randomness and Weakly Complete Problems. [Report]
![[thumbnail of Full Text]](https://eprints.illc.uva.nl/style/images/fileicons/text.png) |
Text (Full Text)
CT-1994-09.text.ps.gz Download (77kB) |
|
Text (Abstract)
CT-1994-09.abstract.txt Download (1kB) |
Abstract
We introduce and study resource bounded random sets based on Lutz's
concept of resource bounded measure. We concentrate on n^crandomness
(c >= 2) which corresponds to the polynomial time bounded (p)measure
of Lutz, and which is adequate for studying the internal and
quantitative structure of E = DTIME(2^lin). However we will also comment
on E_2 = DTIME(2^pol) and its corresponding (p_2)measure. First
we show that the class of n^crandom sets has pmeasure 1. This provides
a new, simplified approach to pmeasure 1results. Next we compare
randomness with genericity, and we show that n^(c+1)random sets are
n^cgeneric, whereas the converse fails. From the former
we conclude that n^crandom sets are not pbttcomplete for E. Our technical
main results describe the distribution of the n^crandom sets under
pmreducibility. We show that every n^crandom set in E has n^krandom
predecessors in E for any k >= 1, whereas the amount of randomness of the
successors is bounded. We apply this result to answer a question raised by
Lutz: We show that the class of weakly complete sets has measure 1 in E and
that there are weakly complete problems which are not pbttcomplete for E.
| Item Type: | Report |
|---|---|
| Report Nr: | CT-1994-09 |
| Series Name: | Computation and Complexity Theory (CT) |
| Year: | 1994 |
| Date Deposited: | 12 Oct 2016 14:39 |
| Last Modified: | 12 Oct 2016 14:39 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1057 |
Actions (login required)
 |
View Item |
