Results 1  10
of
20
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 ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
(Show Context)
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
Five views of hypercomputation
"... We overview different approaches to the study of hypercomputation and other investigations on the plausibility of the physical Church–Turing thesis. We propose five thesis to classify investigation in this area. Sly does it. Tiptoe catspaws. Slide and creep. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We overview different approaches to the study of hypercomputation and other investigations on the plausibility of the physical Church–Turing thesis. We propose five thesis to classify investigation in this area. Sly does it. Tiptoe catspaws. Slide and creep.
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
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. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
Output concepts for accelerated Turing machines
, 2009
"... The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discu ..."
Abstract
 Add to MetaCart
The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discussion of either the possible actual use by such a machine of an infinite amount of space, or the difficulty (even if only a finite amount of space is used) of defining an outcome for machines acting like Thomson’s lamp. It is the authors’ impression that insufficient attention has been paid to introducing a clearly defined counterpart for ATMs of the halting/nonhalting dichotomy for classical Turing computation. This paper tackles the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. Nonstandard integers appear quite useful in this regard and we describe several models of computation using filters.
Turing's titanic machine?  Embodied and disembodied computing at the Turing Centenary
, 2012
"... ..."
1 DEFINABILITY IN THE REAL UNIVERSE ∗
"... Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics w ..."
Abstract
 Add to MetaCart
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory. “If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.”
Zeno Squeezing of Cellular Automata
 INT. JOURN. OF UNCONVENTIONAL COMPUTING, VOL. 6, PP. 399–416
, 2010
"... ..."
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
 Add to MetaCart
(Show Context)
We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
12345efghi UNIVERSITY OF WALES SWANSEA REPORT SERIES
"... Newtonian mechanics and infinitely parallel computation by ..."