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Classical recursion theory
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Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.Abstract:
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.read more
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Effective fractal dimension: foundations and applications
John M. Hitchcock,Jack H. Lutz +1 more
TL;DR: It is shown that packing dimension, despite the greater complexity of its definition, can also be effectivized using gales and that the constructive dimensions can be characterized using constructive entropy rates, and that degrees of arbitrary dimension and strong dimension exist within exponential time.
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Alan Turing and the Mathematical Objection
TL;DR: Logico-mathematical reasons, stemming from his own work, helped to convince Alan Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer.
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On the hardness of analyzing probabilistic programs
TL;DR: The hardness of deciding Probabilistic termination as well as the hardness of approximating expected values and (co)variances for probabilistic programs are studied and covariances apply to variances as well.
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Distinctive signatures of recursion
TL;DR: It is proposed that only a definition focused on representational abilities allows the prediction of specific behavioural traits that enable us to distinguish recursion from non-recursive iteration and from hierarchical embedding.
Journal ArticleDOI
Revising Type-2 Computation and Degrees of Discontinuity
TL;DR: The present work compares and unifies different relaxed notions of computability to cover also discontinuous functions based on the concept of the jump of a representation: both a TTE-counterpart to the well known recursion-theoretic jump on Kleene's Arithmetical Hierarchy of hypercomputation and a formalization of revising computation in the sense of Shoenfield.