Resource bounded randomness and weakly complete problems
We introduce and study resource bounded random sets based on Lutz's concept of resource bounded measure ([5, 6]). We concentrate on nc-randomness (c ≥ 2) which corresponds to the polynomial time bounded (p-) measure of Lutz, and which is adequate for studying the internal and quantative structu...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Chapter/Article |
| Language: | English |
| Published: |
1994
|
| In: |
Algorithms and computation
Year: 1994, Pages: 369-377 |
| DOI: | 10.1007/3-540-58325-4_201 |
| Online Access: | Verlag: https://dx.doi.org/10.1007/3-540-58325-4_201
|
| Author Notes: | Klaus Ambos-Spies, Sebastiaan A. Terwijn, Zheng Xizhong |
| Summary: | We introduce and study resource bounded random sets based on Lutz's concept of resource bounded measure ([5, 6]). We concentrate on nc-randomness (c ≥ 2) which corresponds to the polynomial time bounded (p-) measure of Lutz, and which is adequate for studying the internal and quantative structure of E = DTIME(2lin). First we show that the class of nc-random sets has p-measure 1. This provides a new, simplified approach to p-measure 1-results. Next we compare randomness with genericity (in the sense of [1, 2]) and we show that nc+1-random sets are nc-generic, whereas the converse fails. From the former we conclude thatnc-random sets are not p-btt-complete for E. Our technical main results describe the distribution of the nc-random sets under p-m-reducibility. We show that every nc-random set in E has nk-random 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 [8]: We show that the class of weakly complete sets has measure 1 in E and that there are weakly complete problems which are not p-btt-complete for E. |
|---|---|
| Item Description: | Elektronische Reproduktion der Druck-Ausgabe 1. Januar 2005 Gesehen am 31.05.2023 |
| Physical Description: | Online Resource |
| ISBN: | 9783540486534 |
| DOI: | 10.1007/3-540-58325-4_201 |