Feasible Depth

  • David Doty
  • Philippe Moser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

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.

Keywords

dimension depth randomness polynomial-time finite-state 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • David Doty
    • 1
  • Philippe Moser
    • 2
  1. 1.Department of Computer Science, Iowa State University, Ames, IA 50011USA
  2. 2.Dept de Informática e Ingeniería de Sistemas, Centro Politécnico Superior, ZaragozaSpain

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