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Phase Transition and Strong Predictability

  • Conference paper
Unconventional Computation and Natural Computation (UCNC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8553))

Abstract

The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425–434, 2008], where we introduced the notion of thermodynamic quantities into AIT. These quantities are real functions of temperature T > 0. The values of all the thermodynamic quantities diverge when T exceeds 1. This phenomenon corresponds to phase transition in statistical mechanics. In this paper we introduce the notion of strong predictability for an infinite binary sequence and then apply it to the partition function Z(T), which is one of the thermodynamic quantities in AIT. We then reveal a new computational aspect of the phase transition in AIT by showing the critical difference of the behavior of Z(T) between T = 1 and T < 1 in terms of the strong predictability for the base-two expansion of Z(T).

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Author information

Authors and Affiliations

  1. Research and Development Initiative, Chuo University, 1–13–27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Kohtaro Tadaki

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  1. Kohtaro Tadaki
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Correspondence to Kohtaro Tadaki .

Editor information

Editors and Affiliations

  1. Santa Barbara College of Engineering, University of California, Santa Barbara, California, USA

    Oscar H. Ibarra

  2. University of Western Ontario, London, Ontario, Canada

    Lila Kari

  3. University of Western Ontario, London, Ontario, Canada

    Steffen Kopecki

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Tadaki, K. (2014). Phase Transition and Strong Predictability. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_28

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  • DOI: https://doi.org/10.1007/978-3-319-08123-6_28

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08122-9

  • Online ISBN: 978-3-319-08123-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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