Feasible Depth

David Doty; Philippe Moser

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Feasible Depth

David Doty·Philippe Moser

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Abstract

This paper introduces two complexity-theoretic formulations of Bennett's logical depth: finite-state depth and polynomial-time depth. It is shown that for both formulations, trivial and random infinite sequences are shallow, and a slow growth law holds, implying that deep sequences cannot be created easily from shallow sequences. Furthermore, the E analogue of the halting language is shown to be polynomial-time deep, by proving a more general result: every language to which a nonnegligible subset of E can be reduced in uniform exponential time is polynomial-time deep.

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BibTeX RIS

David Doty, Philippe Moser. 2007-04-11. Feasible Depth. https://arxiv.org/abs/cs/0701123

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