Resource-bounded balanced genericity, stochasticity and weak randomness

  • Klaus Ambos-Spies
  • Elvira Mayordomo
  • Yongge Wang
  • Xizhong Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


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.


Selection Function Complexity Theory Initial Segment Prediction Function Weak Notion 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  • Elvira Mayordomo
    • 2
  • Yongge Wang
    • 1
  • Xizhong Zheng
    • 1
  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Dept. Ingeniería InformáticaUniversidad de ZaragozaZaragozaSpain

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