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Computability and Randomness$
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André Nies

Print publication date: 2009

Print ISBN-13: 9780199230761

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230761.001.0001

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Diagonally noncomputable functions

Diagonally noncomputable functions

(p.144) 4 Diagonally noncomputable functions
Computability and Randomness

André Nies

Oxford University Press

This chapter motivates the interaction from randomness to computability. As an example of this interaction it shows how to use Martin–Löf randomness to give a simple injury-free solution to Post's problem as a result of Kucera. The chapter studies diagonally noncomputable (d.n.c.) functions and looks closely at two valued d.n.c. functions. The former can be used for a more general solution of Post's problem and an injury free proof of the Friedberg–Muchnik theorem. The chapter then matches n-randomness with n-fixed point freeness.

Keywords:   diagonally noncomputable function, initial segment complexity, Post's problem, Friedberg–Muchnik theorem, injury freeness, PA completeness, n-randomness

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