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Conference on Computability in Europe

CiE 2007: Computation and Logic in the Real World pp 228–237Cite as

Feasible Depth

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University, Ames, IA 50011, USA

    David Doty

  2. Dept de Informática e Ingeniería de Sistemas, Centro Politécnico Superior, Zaragoza, Spain

    Philippe Moser

Authors
  1. David Doty
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  2. Philippe Moser
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Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

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© 2007 Springer-Verlag Berlin Heidelberg

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Doty, D., Moser, P. (2007). Feasible Depth. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_24

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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