# Physical Hypercomputation and the Church–Turing Thesis

@article{Shagrir2003PhysicalHA, title={Physical Hypercomputation and the Church–Turing Thesis}, author={Oron Shagrir and Itamar Pitowsky}, journal={Minds and Machines}, year={2003}, volume={13}, pages={87-101} }

We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.

## 73 Citations

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- Philosophy, Computer ScienceCiE
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The Church-Turing thesis cannot be proved in the same sense that a mathematical proposition is provable, however, it can be refuted by an example of a function which is not Turing computable, but is nevertheless calculable by some procedure that is intuitively acceptable.

### Hypercomputation and the Physical Church‐Turing Thesis

- Philosophy, Computer ScienceThe 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,…

### What is the Church-Turing Thesis?

- Computer Science
- 2020

We aim to put some order to the multiple interpretations of the ChurchTuring Thesis and to the different approaches taken to prove or disprove it. [Answer:] Rosser and its inventor proved that its…

### Oracle Turing machines faced with the verification problem

- Computer Science
- 2012

An analysis of the verification problem is proposed in order to show that it does not explicitly dispute the strategy about a physical construction of an oracle Turing machine.

### The Physical Church–Turing Thesis: Modest or Bold?

- PhilosophyThe British Journal for the Philosophy of Science
- 2011

It is proposed to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function.

### How to Make a Meaningful Comparison of Models: The Church–Turing Thesis Over the Reals

- PhilosophyMinds and Machines
- 2016

It is argued that it is possible in both cases to defend an equivalent of the Church–Turing thesis over the reals, and some methodological caveats on the comparison of different computational models are learned.

### Physical Computability Theses

- Computer Science
- 2020

All three variants of the physical Church-Turing Thesis (PCTT) are concluded that all three variants are best viewed as open empirical hypotheses.

### A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

- PhysicsSynthese
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It is suggested 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.

### A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

- Physics
- 2015

This essay will honour Istvan’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 Nemeti and David might be complemented by a quantum-information-theoretic communication protocol.

### Relativistic computation

- Computer Science
- 2017

This chapter focuses on relativistic computers and on their challenge to the physical Church-Turing thesis (PhCT), the belief that whatever physical computing device or physical thought experiment that will be designed by any future civilization, it will always be simulateable by a Turing machine, in some sense.

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