Hypercomputation and the physical church-Turing thesis

Abstract
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, more than a logico-mathematical, proposition. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be affected. Therefore, Thesis P is not essentially different from the standard Church-Turing Thesis. 1 Introduction 2 Computability and incomputability 3 The physical interpretation of the Church-Turing Thesis 4 Supertasks and infinite computation 5 Computation on non-well-founded domains 6 Analog computation 7 Quantum computation 8 Retrocausal computation 9 Conclusions.
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Citations of this work BETA
Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
Gualtiero Piccinini (2011). The Physical Church–Turing Thesis: Modest or Bold? British Journal for the Philosophy of Science 62 (4):733 - 769.

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