# Hypercomputation: computing more than the Turing machine

@article{Ord2002HypercomputationCM, title={Hypercomputation: computing more than the Turing machine}, author={Toby Ord}, journal={ArXiv}, year={2002}, volume={math.LO/0209332} }

Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation that can compute more than the Turing machine and addresses their implications. In this report, I survey much of the work that has been done on hypercomputation, explaining how such non-classical models fit into the classical theory of computation and…

## 78 Citations

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

- PhilosophyArXiv
- 2012

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.

Practical Intractability: A Critique of the Hypercomputation Movement

- PhilosophyMinds and Machines
- 2013

This work presents a more mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally.

A hypercomputational alien q

- Computer Science
- 2006

A conceptual framework for power comparison is proposed, by linking computational models to hypothetical physical devices, and some mathematical notions of relative computational power are deduced, allowing for the comparison of arbitrary models over arbitrary domains.

Transfinite Turing machines

- Computer Science

The construction of a new model of infinite computability is the key to understand and find algorithms that require an infinite number of steps to compute the solution.

The Diagonal Method and Hypercomputation

- MathematicsThe British Journal for the Philosophy of Science
- 2005

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 physical and philosophical implications of the Church-Turing Thesis

- Philosophy
- 2004

This research project is an investigation into the physical and philosophical implications of the Church-Turing Thesis [CT], and its relationship to hypercomputation. This thesis has been subject to…

A Hypercomputation in Brouwer's Constructivism

- Computer ScienceArXiv
- 2014

This paper proposes a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive, and refers to models of computation which go beyond Church-Turing thesis.

A tese de Church-Turing

- Computer Science
- 2012

A brief introduction to the Turing thesis is made, and a commented partial translation of the relevant section of Turing's original 1936-37 article "On computable numbers, with an applica- tion to the Entscheidungsproblem" is included, where it is possible to understand how the Turing machine came to be.

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