|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Noncomputable functions in the Blum-Shub-Smale model | | Wesley Calvert
; Ken Kramer
; Russell Miller
; | | Date: |
6 May 2011 | | Abstract: | Working in the Blum-Shub-Smale model of computation on the real numbers, we
answer several questions of Meer and Ziegler. First, we show that, for each
natural number d, an oracle for the set of algebraic real numbers of degree at
most d is insufficient to allow an oracle BSS-machine to decide membership in
the set of algebraic numbers of degree d + 1. We add a number of further
results on relative computability of these sets and their unions. Then we show
that the halting problem for BSS-computation is not decidable below any
countable oracle set, and give a more specific condition, related to the
cardinalities of the sets, necessary for relative BSS-computability. Most of
our results involve the technique of using as input a tuple of real numbers
which is algebraically independent over both the parameters and the oracle of
the machine. | | Source: | arXiv, 1105.1380 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER