Resource-bounded balanced genericity, stochasticity and weak randomness

We introduce balanced t(n)-genericity which is a refinement of the genericity concept of Ambos-Spies, Fleischhack and Huwig [2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasti...

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Bibliographic Details
Main Authors: Ambos-Spies, Klaus (Author) , Mayordomo, Elvira (Author) , Wang, Yongge (Author) , Zheng, Xizhong (Author)
Format: Chapter/Article Conference Paper
Language:English
Published: 1996
In: Proceedings
Year: 1996, Pages: 63-74
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Author Notes:Klaus Ambos-Spies, Elvira Mayordomo, Yongge Wang, Xizhong Zheng
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Summary:We introduce balanced t(n)-genericity which is a refinement of the genericity concept of Ambos-Spies, Fleischhack and Huwig [2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity [6]. By uniformly describing these concepts and weaker notions of stochasticity introduced by Wilber [19] and Ko [11] in terms of prediction functions, we clarify the relations among these resource-bounded stochasticity concepts. Moreover, we give descriptions of these concepts in the framework of Lutz's resource-bounded measure theory [13] based on martingales: We show that t(n)-stochasticity coincides with a weak notion of t(n)-randomness based on so-called simple martingales but that it is strictly weaker than t(n)-randomness in the sense of Lutz.
Item Description:Elektronische Reproduktion der Druck-Ausgabe 1. Januar 2005
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Physical Description:Online Resource
ISBN:9783540497233