Integer valued betting strategies and Turing degrees

ISCAS OpenIR

	Integer valued betting strategies and Turing degrees
	Barmpalias, G; Downey, RG; McInerney, M
	2015
发表期刊	JOURNAL OF COMPUTER AND SYSTEM SCIENCES
ISSN	0022-0000
卷号	81 期号:7 页码:1387-1412
摘要	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.
收录类别	SCI
关键词	Martingales Algorithmic Randomness Betting Strategies Turing Degrees
部门归属	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.
语种	英语
WOS记录号	WOS:000356644600018
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/17434
专题	中国科学院软件研究所
推荐引用方式 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.

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