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  1. Effective Physical Processes and Active Information in Quantum Computing.Ignazio Licata - 2007 - Quantum Biosystems 1 (1):51-65.
    The recent debate on hypercomputation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics.We propose here the idea of “effective physical process” as the essentially physical notion of computation. By using the Bohm and Hiley active information concept we analyze the differences between the standard form (quantum gates) and the non-standard one (adiabatic and morphogenetic) of Quantum Computing, and we point out how its Super-Turing potentialities derive from an incomputable information (...)
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  • Recursive analysis of singular ordinary differential equations.Peter Buser & Bruno Scarpellini - 2010 - Annals of Pure and Applied Logic 162 (1):20-35.
    We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations.
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  • Turing: The Great Unknown.Aurea Anguera, Juan A. Lara, David Lizcano, María-Aurora Martínez, Juan Pazos & F. David de la Peña - 2020 - Foundations of Science 25 (4):1203-1225.
    Turing was an exceptional mathematician with a peculiar and fascinating personality and yet he remains largely unknown. In fact, he might be considered the father of the von Neumann architecture computer and the pioneer of Artificial Intelligence. And all thanks to his machines; both those that Church called “Turing machines” and the a-, c-, o-, unorganized- and p-machines, which gave rise to evolutionary computations and genetic programming as well as connectionism and learning. This paper looks at all of these and (...)
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  • Undecidability through Fourier series.Peter Buser & Bruno Scarpellini - 2016 - Annals of Pure and Applied Logic 167 (7):507-524.
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