1,091 research outputs found
A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer
There exists a growing literature on the so-called physical Church-Turing
thesis in a relativistic spacetime setting. The physical Church-Turing thesis
is the conjecture that no computing device that is physically realizable (even
in principle) can exceed the computational barriers of a Turing machine. By
suggesting a concrete implementation of a beyond-Turing computer in a spacetime
setting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how an
appreciation of the physical Church-Turing thesis necessitates the confluence
of mathematical, computational, physical, and indeed cosmological ideas. In
this essay, I will honour Istv\'an's seventieth birthday, as well as his
longstanding interest in, and his seminal contributions to, this field going
back to as early as 1987 by modestly proposing how the concrete implementation
in N\'emeti and D\'avid (2006) might be complemented by a
quantum-information-theoretic communication protocol between the computing
device and the logician who sets the beyond-Turing computer a task such as
determining the consistency of Zermelo-Fraenkel set theory. This suggests that
even the foundations of quantum theory and, ultimately, quantum gravity may
play an important role in determining the validity of the physical
Church-Turing thesis.Comment: 27 pages, 5 figures. Forthcoming in Synthese. Matches published
versio
Can a computer be "pushed" to perform faster-than-light?
We propose to "boost" the speed of communication and computation by immersing
the computing environment into a medium whose index of refraction is smaller
than one, thereby trespassing the speed-of-light barrier.Comment: 7 pages, 1 figure, presented at the UC10 Hypercomputation Workshop
"HyperNet 10" at The University of Tokyo on June 22, 201
Zeno machines and hypercomputation
This paper reviews the Church-Turing Thesis (or rather, theses) with
reference to their origin and application and considers some models of
"hypercomputation", concentrating on perhaps the most straight-forward option:
Zeno machines (Turing machines with accelerating clock). The halting problem is
briefly discussed in a general context and the suggestion that it is an
inevitable companion of any reasonable computational model is emphasised. It is
hinted that claims to have "broken the Turing barrier" could be toned down and
that the important and well-founded role of Turing computability in the
mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in
July and in November 2005. To appear in Theoretical Computer Scienc
The Computational Power of Minkowski Spacetime
The Lorentzian length of a timelike curve connecting both endpoints of a
classical computation is a function of the path taken through Minkowski
spacetime. The associated runtime difference is due to time-dilation: the
phenomenon whereby an observer finds that another's physically identical ideal
clock has ticked at a different rate than their own clock. Using ideas
appearing in the framework of computational complexity theory, time-dilation is
quantified as an algorithmic resource by relating relativistic energy to an
th order polynomial time reduction at the completion of an observer's
journey. These results enable a comparison between the optimal quadratic
\emph{Grover speedup} from quantum computing and an speedup using
classical computers and relativistic effects. The goal is not to propose a
practical model of computation, but to probe the ultimate limits physics places
on computation.Comment: 6 pages, LaTeX, feedback welcom
Closed Timelike Curves in Relativistic Computation
In this paper, we investigate the possibility of using closed timelike curves
(CTCs) in relativistic hypercomputation. We introduce a wormhole based
hypercomputation scenario which is free from the common worries, such as the
blueshift problem. We also discuss the physical reasonability of our scenario,
and why we cannot simply ignore the possibility of the existence of spacetimes
containing CTCs.Comment: 17 pages, 5 figure
Effective Physical Processes and Active Information in Quantum Computing
The recent debate on hypercomputation has arisen 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 source in accordance with Bell's constraints.
On condition that we give up the formal concept of "universality", the
possibility to realize quantum oracles is reachable. In this way computation is
led back to the logic of physical world.Comment: 10 pages; Added references for sections 2 and
Note on a reformulation of the strong cosmic censor conjceture based on computability
In this letter we provide a reformulation of the strong cosmic censor
conjecture taking into account recent results on Malament--Hogarth space-times.
We claim that the strong version of the cosmic censor conjecture can be
formulated by postulating that a physically relevant space-time is either
globally hyperbolic or possesses the Malament--Hogarth property. But it is
known that a Malament--Hogarth space-time in principle is capable for
performing non-Turing computations such as checking consistency of ZFC set
theory. In this way we get an intimate conjectured link between the cosmic
censorship scenario and computability theory.Comment: LaTeX, 9 pages, 1 eps-figure; minor typos corrected and journal
reference adde
Some Thoughts on Hypercomputation
Hypercomputation is a relatively new branch of computer science that emerged
from the idea that the Church--Turing Thesis, which is supposed to describe
what is computable and what is noncomputable, cannot possible be true. Because
of its apparent validity, the Church--Turing Thesis has been used to
investigate the possible limits of intelligence of any imaginable life form,
and, consequently, the limits of information processing, since living beings
are, among others, information processors. However, in the light of
hypercomputation, which seems to be feasibly in our universe, one cannot impose
arbitrary limits to what intelligence can achieve unless there are specific
physical laws that prohibit the realization of something. In addition,
hypercomputation allows us to ponder about aspects of communication between
intelligent beings that have not been considered befor
Non-classical computing: feasible versus infeasible
Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future
- âŠ