Feasible Depth

This paper introduces two complexity-theoretic formulations of Bennett’s computational 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.

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: David Doty, Philippe Moser
• Keywords: Bennett’s Computational Depth, CIE 2007, Polynomial-time Depth, Random Infinite Sequences