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New computational paradigms

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The introduction discusses the necessity of the concept of Computably Enumerable (CiE) sets, followed by various explorations in computational theory. Topics include the Solovay and Strong Weak Truth Table degrees, the Fan Theorem, continuous semantics for strong normalization, and advancements in membrane computing. The text delves into comparing computational models, the implications of recombinant DNA in formal languages, and the principles of quantum computing. It also addresses symbol grounding in connectionist models and the complexity of inductive definability. Further discussions cover a logical approach to abstract algebra, Schnorr dimension, and abstract geometrical computation, emphasizing Turing-computing ability and undecidability. The annotation highlights computability in geometry, a language for sequential real number computation, and the intricacies of Borel ranks. It also examines various aspects of model theory, definability in enumeration degrees, and proof mining in functional analysis. Additional topics include the power of mobility in membrane computing, the complexity of algorithms, and the relationship between approximation problems and PCPs. The text presents insights into the computational complexity of sandpiles, recursion, and formalizing arithmetic in type theory. Lastly, it explores new algorithmic paradigms, computability in discrete dynamical systems, and the transfinite action of Turing mach

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New computational paradigms, Barry S. Cooper

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2005
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