Institutional Repository
| Integer valued betting strategies and Turing degrees | |
| Barmpalias, G; Downey, RG; McInerney, M | |
| 2015 | |
| Source | JOURNAL OF COMPUTER AND SYSTEM SCIENCES
 |
| ISSN | 0022-0000 |
| Volume | 81Issue:7Pages:1387-1412 |
| English Abstract | Betting strategies are often expressed formally as martingales. A martingale is called integer-valued if each bet must be an integer value. Integer-valued strategies correspond to the fact that in most betting situations, there is a minimum amount that a player can bet. According to a well known paradigm, algorithmic randomness can be founded on the notion of betting strategies. A real X is called integer-valued random if no effective integer-valued martingale succeeds on X. It turns out that this notion of randomness has interesting interactions with genericity and the computably enumerable degrees. We investigate the computational power of the integer-valued random reals in terms of standard notions from computability theory. (C) 2015 Elsevier Inc. All rights reserved.; Betting strategies are often expressed formally as martingales. A martingale is called integer-valued if each bet must be an integer value. Integer-valued strategies correspond to the fact that in most betting situations, there is a minimum amount that a player can bet. According to a well known paradigm, algorithmic randomness can be founded on the notion of betting strategies. A real X is called integer-valued random if no effective integer-valued martingale succeeds on X. It turns out that this notion of randomness has interesting interactions with genericity and the computably enumerable degrees. We investigate the computational power of the integer-valued random reals in terms of standard notions from computability theory. (C) 2015 Elsevier Inc. All rights reserved. |
| Indexed Type | SCI |
| Keyword | Martingales Algorithmic Randomness Betting Strategies Turing Degrees |
| Department | Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Victoria Univ, Sch Math Stat & Operat Res, Wellington, New Zealand. |
| Language | 英语 |
| WOS ID | WOS:000356644600018 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/17434 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Barmpalias, G,Downey, RG,McInerney, M. Integer valued betting strategies and Turing degrees[J]. JOURNAL OF COMPUTER AND SYSTEM SCIENCES,2015,81(7):1387-1412. |
| APA | Barmpalias, G,Downey, RG,&McInerney, M.(2015).Integer valued betting strategies and Turing degrees.JOURNAL OF COMPUTER AND SYSTEM SCIENCES,81(7),1387-1412. |
| MLA | Barmpalias, G,et al."Integer valued betting strategies and Turing degrees".JOURNAL OF COMPUTER AND SYSTEM SCIENCES 81.7(2015):1387-1412. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 1-s2.0-S002200001500（849KB） | 开放获取 | License | Application Full Text | |||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment