Zeno machines and hypercomputation

@article{Potgieter2006ZenoMA,
  title={Zeno machines and hypercomputation},
  author={Petrus H. Potgieter},
  journal={Theor. Comput. Sci.},
  year={2006},
  volume={358},
  pages={23-33}
}
  • P. Potgieter
  • Published 6 December 2004
  • Business
  • Theor. Comput. Sci.

Hypercomputation: Towards an extension of the classical notion of Computability?

TLDR
This thesis makes an analysis of the concept of Hypercomputation and of some hypermachines and attention is given to the possible physical realization of these machines and their usefulness.

A Brief Critique of Pure Hypercomputation

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just

On the Possibilities of Hypercomputing Supertasks

TLDR
It is concluded that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection or re-interpretation of the Church-Turing thesis in its traditional interpretation.

Approximate Outputs of Accelerated Turing Machines Closest to Their Halting Point

TLDR
This paper addresses the issue of defining the output of a machine close or at the halting point and supports this analysis by reasoning on Thomson’s paradox and by looking closely the result of the Twin Prime conjecture.

Zeno machines and Running Turing machine for infinite time

TLDR
It is proved that the halting problem algorithm for every Turing-recognizable program and every input cannot be devised whatever method is used to exploit infinite running-time of Turing machine.

Ultrafilter and Non-standard Turing Machines

TLDR
The main problem is the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps, and a modest scheme, using non-standard numbers, is proposed.

Zeno Squeezing of Cellular Automata

TLDR
The main definitions and propositions are surveyed and new results regarding the indeterminism of self-similar cellular automata are added.

Hypercomputing the Mandelbrot Set?

TLDR
The Mandelbrot set is surveyed and two models of decidability over the reals are considered, two over the computable reals (the Russian school and hypercomputation) and a model over the rationals.

Series A Note on Accelerated Turing Machines

In this note we prove that any Turing machine which uses only a finite computational space for every input cannot solve an uncomputable problem even in case it runs in accelerated mode. 1.

Computation as an unbounded process

References

SHOWING 1-10 OF 66 REFERENCES

Hypercomputation by definition

  • B. Wells
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 2004

The Diagonal Method and Hypercomputation

  • Toby OrdT. Kieu
  • Mathematics
    The British Journal for the Philosophy of Science
  • 2005
TLDR
It is demonstrated why a contradiction only occurs if a type of machine can compute its own diagonal function, and why such a situation does not occur for the methods of hypercomputation under attack, andwhy it is unlikely to occur for any other serious methods.

The Myth of Hypercomputation

Under the banner of “hypercomputation” various claims are being made for the feasibility of modes of computation that go beyond what is permitted by Turing computability. In this article it will be

Non-Turing Computations Via Malament–Hogarth Space-Times

TLDR
It is argued that there are several distinguished Church–Turing-type theses (not only one) and validity of some of these theses depend on the background physical theory the authors choose to use, and if they choose classical general relativity theory as their background theory, then certain forms of the Church-Turing thesis cease to be valid.

The Church-Turing Thesis: Breaking the Myth

TLDR
This paper identifies and analyzes the historical reasons for widespread belief that no model of computation more expressive than Turing machines can exist, and presents one such model, Persistent Turing Machines (PTMs), which capture sequential interaction, which is a limited form of concurrency.

Accelerating Turing Machines

TLDR
It is argued that accelerating Turing machines are not logically impossible devices, and there are implications concerning the nature of effective procedures and the theoretical limits of computability.

Hypercomputation and the Physical Church‐Turing Thesis

  • Paolo Cotogno
  • Philosophy, Computer Science
    The British Journal for the Philosophy of Science
  • 2003
A version of the Church‐Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines (‘Thesis P’); in this formulation the Thesis appears an empirical,

Bio-steps beyond Turing.

Classical physics and the Church--Turing Thesis

TLDR
In this article, it is observed that there is fundamental tension between the Extended Church--Turing Thesis and the existence of numerous seemingly intractable computational problems arising from classical physics.

Hypercomputation: philosophical issues

...