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Kojiro Higuchi [7]Kiyoyuki Higuchi [2]K. Higuchi [2]Kōzō Higuchi [1]
Keiji Higuchi [1]
  1.  24
    Propagation of Partial Randomness.Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):742-758.
    Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a (...)
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  2.  13
    Weak Theories of Concatenation and Minimal Essentially Undecidable Theories: An Encounter of WTC\documentclass[12pt]{Minimal} \usepackage{Amsmath} \usepackage{Wasysym} \usepackage{Amsfonts} \usepackage{Amssymb} \usepackage{Amsbsy} \usepackage{Mathrsfs} \usepackage{Upgreek} \setlength{\oddsidemargin}{-69pt} \begin{Document}$${\mathsf{WTC}}$$\end{Document} and S2S\documentclass[12pt]{Minimal} \usepackage{Amsmath} \usepackage{Wasysym} \usepackage{Amsfonts} \usepackage{Amssymb} \usepackage{Amsbsy} \usepackage{Mathrsfs} \usepackage{Upgreek} \setlength{\oddsidemargin}{-69pt} \begin{Document}$${\mathsf{S2S}}$$\end{Document}.Kojiro Higuchi & Yoshihiro Horihata - 2014 - Archive for Mathematical Logic 53 (7-8):835-853.
    We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} (...)
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  3.  10
    Inside the Muchnik Degrees I: Discontinuity, Learnability and Constructivism.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (5):1058-1114.
    Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is equivalent to finite View (...)
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  4.  10
    Effective Strong Nullness and Effectively Closed Sets.Kojiro Higuchi & Takayuki Kihara - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 303--312.
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  5.  16
    On the Strength of Marriage Theorems and Uniformity.Makoto Fujiwara, Kojiro Higuchi & Takayuki Kihara - 2014 - Mathematical Logic Quarterly 60 (3):136-153.
  6.  12
    Inside the Muchnik Degrees II: The Degree Structures Induced by the Arithmetical Hierarchy of Countably Continuous Functions.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (6):1201-1241.
    It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree containing infinitely many finite-2-piecewise degrees, and a finite-2-piecewise degree containing infinitely many finite-Δ20-piecewise degrees 2 denotes the difference of two Πn0 sets), whereas the greatest degrees in (...)
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  7. "Edo" No Hihanteki Keifugaku: Nashonarizumu No Shisōshi.Kōzō Higuchi - 2009 - Perikansha.
    ナショナリズムと親和的関係にある日本通史への欲望を拒否するために、山崎闇斎学派や武士道の語りにおけるナショナルな視線を相対化し、他者性を帯びた「江戸」の自国意識や対中国認識に注目することで、歴史の断面 を記述することの可能性を探る。.
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  8.  6
    Effectively Closed Mass Problems and Intuitionism.Kojiro Higuchi - 2012 - Annals of Pure and Applied Logic 163 (6):693-697.
  9.  8
    Defining a Randomness Notion Via Another.Kojiro Higuchi & Ningning Peng - 2014 - Mathematical Logic Quarterly 60 (4-5):280-288.
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