über die Definition von effektiven Zufallstests

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