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31
On the existence of truly autonomic computing systems and the link with quantum computing
, 2005
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A possible hypercomputational quantum algorithm
 SPIE) PROC. SPIE 5815 219–26
, 2005
"... 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 noncomputable decision problem, Hilbert’s tenth problem; more spe ..."
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Cited by 3 (3 self)
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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 noncomputable 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 (onedimensional) 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.
MATHEMATICAL COMPUTABILITY QUESTIONS FOR SOME CLASSES OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS ORIGINATED FROM HILBERT’S TENTH PROBLEM
, 2005
"... Abstract. Inspired by Quantum Mechanics, we reformulate Hilbert’s tenth problem in the domain of integer arithmetics into problems involving either a set of infinitelycoupled nonlinear differential equations or a class of linear Schrödinger equations with some appropriate timedependent Hamiltonian ..."
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Cited by 2 (2 self)
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Abstract. Inspired by Quantum Mechanics, we reformulate Hilbert’s tenth problem in the domain of integer arithmetics into problems involving either a set of infinitelycoupled nonlinear differential equations or a class of linear Schrödinger equations with some appropriate timedependent Hamiltonians. We then raise the questions whether these two classes of differential equations are computable or not in some computation models of computable analysis. These are nontrivial and important questions given that: (i) not all computation models of computable analysis are equivalent, unlike the case with classical recursion theory; (ii) and not all models necessarily and inevitably reduce computability of real functions to discrete computations on Turing machines. However unlikely the positive answers to our computability questions, their existence should deserve special attention and be satisfactorily settled since such positive answers may also have interesting logical consequence back in the classical recursion theory for the ChurchTuring thesis.
Computational Power of Infinite Quantum Parallelism
 pp.2057–2071 in International Journal of Theoretical Physics vol.44:11
, 2005
"... Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the power of Turing Machines as well as of ‘standard ’ Quantum Computers. These approaches rely on and indicate that quantum mechanics seems to support some infinite variant of class ..."
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Cited by 2 (1 self)
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Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the power of Turing Machines as well as of ‘standard ’ Quantum Computers. These approaches rely on and indicate that quantum mechanics seems to support some infinite variant of classical parallel computing. We compare this new one with other attempts towards hypercomputation by separating (1) its computing capabilities from (2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in analogy to ‘existence’ in mathematical logic. KEY WORDS: Hypercomputation; quantum mechanics; recursion theory; infinite parallelism.
How to acknowledge hypercomputation?
, 2007
"... We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models. ..."
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Cited by 1 (0 self)
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We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
ACCELERATING MACHINES
, 2006
"... This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation me ..."
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This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation methods that have been presented. Finally, we expose the limitations of accelerating machines and conclude by posing some problems for further research.
Does Quantum Mechanics allow for Infinite Parallelism?
, 2004
"... Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of ‘standard ’ Quantum Computers. These approaches rely on and indicate that Quantum Mechanics seems to support some infinite variant of classical paral ..."
Abstract
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Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of ‘standard ’ Quantum Computers. These approaches rely on and indicate that Quantum Mechanics seems to support some infinite variant of classical parallel computing. We compare this new one with other attempts towards hypercomputation by separating 1) its principal computing capabilities from 2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in analogy to ‘existence’ in mathematical logic.
Physical unknowables
, 2008
"... Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unk ..."
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Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.
How to acknowledge hypercomputation?
, 2008
"... We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models. ..."
Abstract
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We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.