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The many forms of hypercomputation
 Applied Mathematics and Computation
, 2006
"... This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. ..."
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Cited by 17 (0 self)
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This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess.
Hypercomputability of quantum adiabatic processes: facts versus prejudices
 http://arxiv.org/quantph/0504101
, 2005
"... Abstract. We give an overview of a quantum adiabatic algorithm for Hilbert’s tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diopha ..."
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Cited by 12 (3 self)
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Abstract. We give an overview of a quantum adiabatic algorithm for Hilbert’s tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the numerical simulation results of some simple Diophantine equations are presented. We also discuss some prejudicial misunderstandings as well as some plausible difficulties faced by the algorithm in its physical implementations. “To believe otherwise is merely to cling to a prejudice which only gives rise to further prejudices... ” 1
An anatomy of a quantum adiabatic algorithm that transcends the Turing computability
 International Journal of Quantum Information
"... We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert’s tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm. Keywords: Quantum adiabatic computation; Turing computability; Hilbert’s tenth problem 1. ..."
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Cited by 10 (1 self)
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We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert’s tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm. Keywords: Quantum adiabatic computation; Turing computability; Hilbert’s tenth problem 1.