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Title:
Integer valued betting strategies and Turing degrees
Author: Barmpalias, G ; Downey, RG ; McInerney, M
Keyword: Martingales ; Algorithmic randomness ; Betting strategies ; Turing degrees
Source: JOURNAL OF COMPUTER AND SYSTEM SCIENCES
Issued Date: 2015
Volume: 81, Issue:7, Pages:1387-1412
Indexed Type: SCI
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.
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.
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.
Language: 英语
WOS ID: WOS:000356644600018
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17434
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Barmpalias, G,Downey, RG,McInerney, M. Integer valued betting strategies and Turing degrees[J]. JOURNAL OF COMPUTER AND SYSTEM SCIENCES,2015-01-01,81(7):1387-1412.
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