Another Example of Higher Order Randomness

Authors:
Verónica Becher;Gregory Chaitin
Affiliations:
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, (1428) Buenos Aires, Argentina;IBM Thomas J. Watson Research Center, P O Box 218, Yorktown Heights, NY 10598, USA
Venue:
Fundamenta Informaticae
Year:
2002

Citing 6
Cited 0

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Abstract

We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability β that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that β is exactly as random as the halting probability of a universal machine equipped with an oracle for the second jump of the halting problem, in spite of the fact that β is defined without considering oracles.