Results for 'Church-Turing Thesis'

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  1.  8
    On Computable Numbers, with an Application to the Entscheidungsproblem.Alonzo Church & A. M. Turing - 1937 - Journal of Symbolic Logic 2 (1):42.
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  2. Alan Turing's Systems of Logic: The Princeton Thesis.Alan Mathison Turing - 2012 - Princeton University Press.
     
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  3. The Church-TuringThesis’ as a Special Corollary of Gödel’s Completeness Theorem.Saul A. Kripke - 2013 - In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press.
    Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, (...)
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  4.  90
    Physical Hypercomputation and the Church–Turing Thesis.Oron Shagrir & Itamar Pitowsky - 2003 - Minds and Machines 13 (1):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 (...)
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  5.  38
    The Interactive Nature of Computing: Refuting the Strong Church–Turing Thesis[REVIEW]Dina Goldin & Peter Wegner - 2008 - Minds and Machines 18 (1):17-38.
    The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new (...)
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  6.  98
    Kripke's Paradox and the Church-Turing Thesis.Mark Sprevak - 2008 - Synthese 160 (2):285-295.
    Kripke (1982, Wittgenstein on rules and private language. Cambridge, MA: MIT Press) presents a rule-following paradox in terms of what we meant by our past use of “plus”, but the same paradox can be applied to any other term in natural language. Many responses to the paradox concentrate on fixing determinate meaning for “plus”, or for a small class of other natural language terms. This raises a problem: how can these particular responses be generalised to the whole of natural language? (...)
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  7. Is the Church-Turing Thesis True?Carol E. Cleland - 1993 - Minds and Machines 3 (3):283-312.
    The Church-Turing thesis makes a bold claim about the theoretical limits to computation. It is based upon independent analyses of the general notion of an effective procedure proposed by Alan Turing and Alonzo Church in the 1930''s. As originally construed, the thesis applied only to the number theoretic functions; it amounted to the claim that there were no number theoretic functions which couldn''t be computed by a Turing machine but could be computed by means of some other (...)
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  8.  62
    The Church-Turing Thesis and Effective Mundane Procedures.Leon Horsten - 1995 - Minds and Machines 5 (1):1-8.
    We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number (...)
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  9. The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733 - 769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by (...)
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  10. Computationalism, The Church–Turing Thesis, and the Church–Turing Fallacy.Gualtiero Piccinini - 2007 - Synthese 154 (1):97-120.
    The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis.
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  11. The Church-Turing Thesis.B. Jack Copeland - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
    There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.
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  12.  87
    Hypercomputation and the Physical Church-Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
    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 (...)
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  13. SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
    Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the (...)
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  14.  55
    In Defense of the Unprovability of the Church-Turing Thesis.Selmer Bringsjord - unknown
    One of us has previously argued that the Church-Turing Thesis (CTT), contra Elliot Mendelson, is not provable, and is — light of the mind’s capacity for effortless hypercomputation — moreover false (e.g., [13]). But a new, more serious challenge has appeared on the scene: an attempt by Smith [28] to prove CTT. His case is a clever “squeezing argument” that makes crucial use of Kolmogorov-Uspenskii (KU) machines. The plan for the present paper is as follows. After covering some (...)
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  15.  1
    Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
    A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This (...)
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  16.  43
    Ingenio E Industria. Guía de Referencia Sobre la Tesis de Turing-Church (Inventiveness and Skili. Reference Guide on Church-Turing Thesis).Enrique Alonso - 1999 - Theoria 14 (2):249-273.
    La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...)
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  17.  53
    How Not To Use the Church-Turing Thesis Against Platonism.R. Urbaniak - 2011 - Philosophia Mathematica 19 (1):74-89.
    Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being (...)
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  18.  26
    Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.Wilfried Sieg - unknown
    Wilfried Sieg. Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.
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  19.  1
    How to Make a Meaningful Comparison of Models: The Church–Turing Thesis Over the Reals.Maël Pégny - 2016 - Minds and Machines 26 (4):359-388.
    It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension (...)
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  20. On the Provability, Veracity, and AI-Relevance of the Church-Turing Thesis.Selmer Bringsjord & Konstantine Arkoudas - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 68-118.
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  21. The Church-Turing Thesis: A Last Vestige of a Failed Mathematical Program.Carol Cleland - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 119-146.
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  22. A Natural Axiomatization of Computability and Proof of Church's Thesis.Nachum Dershowitz & Yuri Gurevich - 2008 - Bulletin of Symbolic Logic 14 (3):299-350.
    Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of (...)
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  23. Church's Thesis and the Conceptual Analysis of Computability.Michael Rescorla - 2007 - Notre Dame Journal of Formal Logic 48 (2):253-280.
    Church's thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing's work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church's thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing's work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we (...)
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  24. The Church-Turing Thesis: Its Nature and Status.Antony Galton - 1996 - In P. J. R. Millican & A. Clark (eds.), Machines and Thought: The Legacy of Alan Turing, Volume 1. Clarendon Press.
     
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  25. The Church-Turing Thesis and Hyper-Computation.O. Shagrir & I. Pitowsky - forthcoming - Minds and Machines.
  26.  41
    The Physical Church-Turing Thesis: Modest or Bold?G. Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
  27.  1
    On Analogues of the Church–Turing Thesis in Algorithmic Randomness.P. Porter Christopher - 2016 - Review of Symbolic Logic 9 (3):456-479.
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  28. Refuting the Strong Church-Turing Thesis: The Interactive Nature of Computing.D. Goldin & P. Wegner - 2008 - Minds and Machines 18 (1):17-38.
     
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  29. And the Church-Turing Thesis.Bhupinder Singh & V. I. I. Gödel’S. Theorem - 2006 - Studia Logica 82 (1.03 pt).
     
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  30.  34
    Wittgenstein Versus Turing on the Nature of Church's Thesis.S. G. Shanker - 1987 - Notre Dame Journal of Formal Logic 28 (4):615-649.
  31.  35
    Some Notes on Church's Thesis and the Theory of Games.Luca Anderlini - 1990 - Theory and Decision 29 (1):19-52.
  32.  32
    Reflections on Gödel's and Gandy's Reflections on Turing's Thesis.David Israel - 2002 - Minds and Machines 12 (2):181-201.
    We sketch the historical and conceptual context of Turing's analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland's views.
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  33.  24
    Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem. [REVIEW]Alonzo Church - 1937 - Journal of Symbolic Logic 2 (1):42-43.
  34.  37
    The Use of Dots as Brackets in Church's System.A. M. Turing - 1942 - Journal of Symbolic Logic 7 (4):146-156.
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  35.  15
    A Formal Theorem in Church's Theory of Types.M. H. A. Newman & A. M. Turing - 1942 - Journal of Symbolic Logic 7 (1):28-33.
  36.  1
    Turing A. M.. On Computable Numbers, with an Application to the Entscheidungs Problcm. Proceedings of the London Mathematical Society, 2 S. Vol. 42 , Pp. 230–265. [REVIEW]Alonzo Church - 1937 - Journal of Symbolic Logic 2 (1):42-43.
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  37. Les deux formes de la thèse de Church-Turing et l’épistémologie du calcul.Maël Pégny - 2012 - Philosophia Scientiae 16 (3):39-67.
    La thèse de Church-Turing stipule que toute fonction calculable est calculable par une machine de Turing. En distinguant, à la suite de nombreux auteurs, une forme algorithmique de la thèse de Church-Turing portant sur les fonctions calculables par un algorithme d’une forme empirique de cette même thèse, portant sur les fonctions calculables par une machine, il devient possible de poser une nouvelle question : les limites empiriques du calcul sont-elles identiques aux limites des algorithmes? Ou existe-t-il un moyen (...)
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  38.  57
    Effective Computation by Humans and Machines.Oron Shagrir - 2002 - Minds and Machines 12 (2):221-240.
    There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing (...)
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  39. Philosophy of Mind Is (in Part) Philosophy of Computer Science.Darren Abramson - 2011 - Minds and Machines 21 (2):203-219.
    In this paper I argue that whether or not a computer can be built that passes the Turing test is a central question in the philosophy of mind. Then I show that the possibility of building such a computer depends on open questions in the philosophy of computer science: the physical Church-Turing thesis and the extended Church-Turing thesis. I use the link between the issues identified in philosophy of mind and philosophy of computer science to respond (...)
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  40. On the Possibilities of Hypercomputing Supertasks.Vincent C. Müller - 2011 - Minds and Machines 21 (1):83-96.
    This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they (...)
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  41.  9
    Symbolic Languages and Natural Structures a Mathematician's Account of Empiricism.Hermann G. W. Burchard - 2005 - Foundations of Science 10 (2):153-245.
    The ancient dualism of a sensible and an intelligible world important in Neoplatonic and medieval philosophy, down to Descartes and Kant, would seem to be supplanted today by a scientific view of mind-in-nature. Here, we revive the old dualism in a modified form, and describe mind as a symbolic language, founded in linguistic recursive computation according to the Church-Turing thesis, constituting a world L that serves the human organism as a map of the Universe U. This methodological distinction (...)
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  42.  16
    Is There a Nonrecursive Decidable Equational Theory?Benjamin Wells - 2002 - Minds and Machines 12 (2):301-324.
    The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, (...)
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  43. Ingenio e Industria. Guía de referencia sobre la Tesis de Turing-Church.Enrique Alonso - 1999 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 14 (2):249-273.
    La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...)
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  44.  35
    What Turing Did After He Invented the Universal Turing Machine.B. Jack Copeland & Diane Proudfoot - 2000 - Journal of Logic, Language and Information 9 (4):491-509.
    Alan Turing anticipated many areas of current research incomputer and cognitive science. This article outlines his contributionsto Artificial Intelligence, connectionism, hypercomputation, andArtificial Life, and also describes Turing's pioneering role in thedevelopment of electronic stored-program digital computers. It locatesthe origins of Artificial Intelligence in postwar Britain. It examinesthe intellectual connections between the work of Turing and ofWittgenstein in respect of their views on cognition, on machineintelligence, and on the relation between provability and truth. Wecriticise widespread and influential misunderstandings of theChurch–Turing (...) and of the halting theorem. We also explore theidea of hypercomputation, outlining a number of notional machines thatcompute the uncomputable. (shrink)
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  45.  92
    Physical Computation: How General Are Gandy's Principles for Mechanisms?B. Jack Copeland & Oron Shagrir - 2007 - Minds and Machines 17 (2):217-231.
    What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. (...)
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  46. Alan Turing's Systems of Logic: The Princeton Thesis.Andrew W. Appel (ed.) - 2012 - Princeton University Press.
    Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing, the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. (...)
     
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  47. Alan Turing and the Mathematical Objection.Gualtiero Piccinini - 2003 - Minds and Machines 13 (1):23-48.
    This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...)
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  48.  68
    Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
    Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...)
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  49.  58
    Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW]Eli Dresner - 2008 - Minds and Machines 18 (3):349-355.
  50.  8
    A Note on the Theorems of Church‐Turing and Trachtenbrot.Michael Deutsch - 1994 - Mathematical Logic Quarterly 40 (3):422-424.
    We sketch proofs of the theorems of Church-Turing and Trachtenbrot using a semi-monomorphic axiomatization.
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