Examinando por Autor "Velez, M"

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    Ítem
    Numerical simulations of a possible hypercomputational quantum algorithm
    (SPRINGER-VERLAG WIEN, 2005-01-01) Sicard, A; Ospina, J; Velez, M; Sicard, A; Ospina, J; Velez, M; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on quantum computations previously constructed by the authors are presented. The hypercomputability of our algorithm is based on the fact that this algorithm could solve a classically non-computable decision problem, the Hilbert's tenth problem. The numerical simulations were realized for three types of Diophantine equations: with and without solutions in non-negative integers, and without solutions by way of various traditional mathematical packages.
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    Ítem
    A possible hypercomputational quantum algorithm
    (SPIE-INT SOC OPTICAL ENGINEERING, 2005-01-01) Sicard, A; Velez, M; Ospina, J; Sicard, A; Velez, M; Ospina, J; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    The term `hypermachine' denotes any data processing device (theoretical or that can be implemented) capable of carrying out tasks that cannot be performed by a Turing machine. We present a possible quantum algorithm for a classically non-computable decision problem, Hilbert's tenth problem; more specifically, we present a possible hypercomputation model based on quantum computation. Our algorithm is inspired by the one proposed by Tien D. Kieu, but we have selected the infinite square well instead of the (one-dimensional) simple harmonic oscillator as the underlying physical system. Our model exploits the quantum adiabatic process and the characteristics of the representation of the dynamical Lie algebra su(1, 1) associated to the infinite square well.