Physical Hypercomputation and the Church–Turing Thesis

  title={Physical Hypercomputation and the Church–Turing Thesis},
  author={Oron Shagrir and Itamar Pitowsky},
  journal={Minds and Machines},
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. 

From Logic to Physics: How the Meaning of Computation Changed over Time

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

  • 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,

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Oracle Turing machines faced with the verification problem

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The Physical Church–Turing Thesis: Modest or Bold?

  • G. Piccinini
  • Philosophy
    The 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.

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

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

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

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.



Computation Beyond the Turing Limit

A simply described but highly chaotic dynamical system called the analog shift map is presented here, which has computational power beyond the Turing limit (super-Turing); it computes exactly like neural networks and analog machines.

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It is argued that mundane procedures can be said to be effective in the same sense in which Turing machine procedures can been said toBe effective, and that mundane Procedures differ from Turing machine Procedures in a fundamental way, viz., the former, but not the latter, generate causal processes.

Two Dogmas of Computationalism

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Beyond the universal Turing machine

An emerging field is described, that of nonclassical computability and non classical computing machinery, and a philosophical defence of its foundations is provided.

Church's Thesis and Principles for Mechanisms

On the Church-Turing thesis

It is suggested that, according to the latest results on classical recursive probabilistic solution of the Halting Problem, such Church-Turing Thesis is asymptotically false.

Alan Turing and the Turing Machine.Turing's Analysis of Computability, and Major Applications of it.The Confluence of Ideas in 1936.Turing in the Land of O.Mathematical Logic and the Origin of Modern Computers

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On Formally Undecidable Propositions of Principia Mathematica and Related Systems

This document is a translation of a large part of Gödel’s proof, where the notation used by Gödel has been largely replaced by other notation.

Undecidability and intractability in theoretical physics.

  • Wolfram
  • Physics
    Physical review letters
  • 1985
Cellular automata are used to provide explicit examples of various formally undecidable and computationally intractable problems and it is suggested that such problems are common in physical models, and some other potential examples are discussed.

On computable numbers, with an application to the Entscheidungsproblem

  • A. Turing
  • Computer Science
    Proc. London Math. Soc.
  • 1937
This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.