A statistical mechanical interpretation of algorithmic information theory. III: Composite systems and fixed points
type: Item
instance of: scholarly article
zbMATH Open document ID: 1250.68136
DOI: 10.1017/S096012951100051X
publication date: 2012-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/0904.0973
Mathematics Subject Classification ID: 68Q30
Mathematics Subject Classification ID: 82B30
Mathematics Subject Classification ID: 82B03
zbMATH DE Number: 6097865
zbMATH Keywords: algorithmic information theory
zbMATH Keywords: statistical mechanics
zbMATH Keywords: composite systems
zbMATH Keywords: fixed points
zbMATH Keywords: thermodynamics
author: Kohtaro Tadaki
MaRDI profile type: Publication
arXiv ID: 0904.0973
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cites work: Statistical physics I. Equilibrium statistical mechanics. Rev. transl. from the Japanese ed. by Morikazu Toda and Nobuhiko Saitô.
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title: A statistical mechanical interpretation of algorithmic information theory. III: Composite systems and fixed points
published in: MSCS. Mathematical Structures in Computer Science
review text: Algorithmic information theory was founded by \textit{R. J. Solomonoff} [Inform. and Control 7, 1--22 (1964; Zbl 0258.68045); ibid. 7, 224--254 (1964; Zbl 0259.68038)] in the 1960s. It was developed independently by \textit{A. N. Kolmogorov} [Probl. Peredaci Inform. 1, No. 1, 3--11 (1965; Zbl 0271.94018)] and \textit{G. Chaitin} [J. Assoc. Comput. Mach. 13, 547--569 (1966; Zbl 0158.25301)]. NEWLINENEWLINENEWLINENEWLINEThe author introduced and developed a statistical mechanical interpretation of algorithmic information theory in [``A statistical mechanical interpretation of algorithmic information theory'', in: A. Beckmann (ed.) et al., Logic and theory of algorithms. Fourth conference on computability in Europe, CiE 2008. Local proceedings. Athens: University of Athens. 425--434 (2008)] and [Ann. Pure Appl. Logic 163, No. 7, 763--774 (2012; Zbl 1247.03088)]. NEWLINENEWLINENEWLINENEWLINEThe principal objective in this paper is to investigate the structure of \(\mathcal{FP}_{w}\) and \(\mathcal{FP}\) in greater detail, where \(\mathcal{FP}\) (\(\mathcal{FP}_{w}\)) denotes the set of all \(T\in(0,1)\) NEWLINEthat \(T\) is (weakly) Chaitin \(T\)-random and \(T\)-compressible.
reviewed by: Hirokazu Nishimura
description: scientific article; zbMATH DE number 6097865