A statistical mechanical interpretation of algorithmic information theory. III: Composite systems and fixed points
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.
scientific article; zbMATH DE number 6097865
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