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über die Definition von effektiven Zufallstests
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  • Published: December 1970

über die Definition von effektiven Zufallstests

Teil II

  • Claus -Peter Schnorr1 

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 15, pages 313–328 (1970)Cite this article

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Summary

We continue the discussion on the definition of random sequences from Part I. We will show that the idea of Kolmogoroff to characterize random sequences by their program complexity can be formulated in such a way as to let this definition coÏncide with the others given in Part I. Another equivalent definition of random sequences can be derived from the games of chance. A sequence is random, if and only if no player who calculates his pool by effective methods can raise his fortune indefinitely when playing on this sequence. Finally we will study transformations which preserve the random property of a sequence. We will prove that the original concept of v. Mises can also be modified in such a manner as to coÏncide with all our other definitions. A sequence is random, if and only if it satisfies the strong law of large numbers and if every sequence obtained from it by a constructive measure-preserving transformation is random, too.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der UniversitÄt des Saarlandes, D-6600, Saarbrücken 15

    Claus -Peter Schnorr

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  1. Claus -Peter Schnorr
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Die Arbeit stellt einen Teil der Habilitationsschrift dar, die der Mathematisch-Naturwissenschaftlichen FakultÄt der UniversitÄt des Saarlandes vom Verfasser vorgelegt wurde.

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Schnorr, C.P. über die Definition von effektiven Zufallstests. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 313–328 (1970). https://doi.org/10.1007/BF00533302

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  • Received: 12 June 1969

  • Issue Date: December 1970

  • DOI: https://doi.org/10.1007/BF00533302

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