Calibrating the complexity of Delta 2 sets via their changes

Andre Nies

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arXiv · 1302.0454

Calibrating the complexity of Delta 2 sets via their changes

Andre Nies

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Abstract

The computational complexity of a Delta 2 set will be calibrated by the amount of changes needed for any of its computable approximations. Firstly, we study Martin-Loef random sets, where we quantify the changes of initial segments. Secondly, we look at c.e. sets, where we quantify the overall amount of changes by obedience to cost functions. Finally, we combine the two settings. The discussions lead to three basic principles on how complexity and changes relate.

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Andre Nies. 2013-02-03. Calibrating the complexity of Delta 2 sets via their changes. https://arxiv.org/abs/1302.0454

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