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Conference on Computability in Europe

CiE 2006: Logical Approaches to Computational Barriers pp 85–93Cite as

Prefix-Like Complexities and Computability in the Limit

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 3988)

Abstract

Computability in the limit represents the non-plus-ultra of constructive describability. It is well known that the limit computable functions on naturals are exactly those computable with the oracle for the halting problem. However, prefix (Kolmogorov) complexities defined with respect to these two models may differ. We introduce and compare several natural variations of prefix complexity definitions based on generalized Turing machines embodying the idea of limit computability, as well as complexities based on oracle machines, for both finite and infinite sequences.

Keywords

  • Kolmogorov complexity
  • limit computability
  • generalized Turing machine
  • non-halting computation

This work was sponsored by SNF grant 200020-107590/1.

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Author information

Authors and Affiliations

  1. IDSIA, Galleria 2, 6928, Manno, Switzerland

    Alexey Chernov & Jürgen Schmidhuber

  2. TU Munich, Boltzmannstr. 3, 85748, Garching, München, Germany

    Jürgen Schmidhuber

Authors
  1. Alexey Chernov
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  2. Jürgen Schmidhuber
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Singleton Park, SA2 8PP, Swansea, United Kingdom

    Arnold Beckmann

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Ulrich Berger

  3. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  4. School of Physical Sciences, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, United Kingdom

    John V. Tucker

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Chernov, A., Schmidhuber, J. (2006). Prefix-Like Complexities and Computability in the Limit. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_9

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  • DOI: https://doi.org/10.1007/11780342_9

  • Publisher Name: Springer, Berlin, Heidelberg

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