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  1. 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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