Search results for 'hypercomputing' (try it on Scholar)

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  1. Vincent C. Müller (2011). On the Possibilities of Hypercomputing Supertasks. Minds and Machines 21 (1):83-96.score: 18.0
    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 are (...)
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  2. Selmer Bringsjord (2004). The Modal Argument for Hypercomputing Minds. Theoretical Computer Science 317.score: 9.0
  3. Paolo Cotogno (2009). A Brief Critique of Pure Hypercomputation. Minds and Machines 19 (3):391-405.score: 6.0
    Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise (...)
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  4. B. Jack Copeland (2002). Hypercomputation. Minds and Machines 12 (4):461-502.score: 6.0
  5. Gordana Dodig-Crnkovic (2011). Significance of Models of Computation, From Turing Model to Natural Computation. Minds and Machines 21 (2):301-322.score: 6.0
    The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and (...)
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  6. Amit Hagar & Alexandre Korolev (2006). Quantum Hypercomputability? Minds and Machines 16 (1):87-93.score: 6.0
    A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.
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  7. Mike Stannett (2003). Computation and Hypercomputation. Minds and Machines 13 (1):115-153.score: 6.0
    Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...)
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  8. Aran Nayebi (forthcoming). Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW] Minds and Machines:1-31.score: 6.0
    For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...)
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  9. Selmer Bringsjord & Michael Zenzen (2002). Toward a Formal Philosophy of Hypercomputation. Minds and Machines 12 (2):241-258.score: 6.0
    Does what guides a pastry chef stand on par, from the standpoint of contemporary computer science, with what guides a supercomputer? Did Betty Crocker, when telling us how to bake a cake, provide an effective procedure, in the sense of `effective' used in computer science? According to Cleland, the answer in both cases is ``Yes''. One consequence of Cleland's affirmative answer is supposed to be that hypercomputation is, to use her phrase, ``theoretically viable''. Unfortunately, though we applaud Cleland's ``gadfly philosophizing'' (...)
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  10. Oron Shagrir & Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.score: 5.0
    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.
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  11. Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.score: 5.0
    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.
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  12. Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.score: 4.0
    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 (...)
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  13. Toby Ord & Tien D. Kieu (2005). The Diagonal Method and Hypercomputation. British Journal for the Philosophy of Science 56 (1):147-156.score: 4.0
    The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation (...)
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  14. Tien D. Kieu (2002). Quantum Hypercomputation. Minds and Machines 12 (4):541-561.score: 4.0
    We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.
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  15. Toby Ord, Hypercomputation: Computing More Than the Turing Machine.score: 4.0
    In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines.
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  16. Philip D. Welch (2004). On the Possibility, or Otherwise, of Hypercomputation. British Journal for the Philosophy of Science 55 (4):739-746.score: 4.0
    We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead (...)
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  17. Carol E. Cleland (2002). On Effective Procedures. Minds and Machines 12 (2):159-179.score: 3.0
    Since the mid-twentieth century, the concept of the Turing machine has dominated thought about effective procedures. This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic. I show that Turing machines cannot live up to their billing as paragons of effective procedure; at best, they may be said to provide us with mere procedure schemas. I argue that the concept of an effective procedure crucially depends upon distinguishing procedures as definite courses (...)
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  18. Amit Hagar & Alex Korolev (2007). Quantum Hypercomputation—Hype or Computation? Philosophy of Science 74 (3):347-363.score: 3.0
    A recent attempt to compute a (recursion‐theoretic) noncomputable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion‐theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.
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  19. B. Jack Copeland & Diane Proudfoot (2000). What Turing Did After He Invented the Universal Turing Machine. Journal of Logic, Language and Information 9 (4):491-509.score: 3.0
    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 thesis (...)
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  20. Toby Ord, The Many Forms of Hypercomputation.score: 3.0
    This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. 2005 Elsevier Inc. All rights reserved.
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  21. E. Mendelson (2005). Selmer Bringsjord and Michael Zenzen. Superminds: People Harness Hypercomputation, and More. Studies in Cognitive Systems, Volume 29. Dordrecht: Kluwer Academic Publishers, 2003. Pp. Xxx + 339. ISBN 1-4020-1094-X. [REVIEW] Philosophia Mathematica 13 (2):228-230.score: 3.0
  22. Martin Davis (2006). Why There is No Such Discipline as Hypercomputation. Applied Mathematics and Computation, Volume 178, Issue 1, 1.score: 3.0
     
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  23. Keith Douglas (2013). Learning to Hypercompute? An Analysis of Siegelmann Networks. In. In Gordana Dodig-Crnkovic Raffaela Giovagnoli (ed.), Computing Nature. 201--211.score: 3.0
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  24. Péter Németi & Gergely Székely (2012). Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity. In. In S. Barry Cooper (ed.), How the World Computes. 528--538.score: 3.0
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  25. B. Jack Copeland & Oron Shagrir (2007). Physical Computation: How General Are Gandy's Principles for Mechanisms? [REVIEW] Minds and Machines 17 (2):217-231.score: 2.0
    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. We (...)
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  26. B. Jack Copeland & Oron Shagrir (2011). Do Accelerating Turing Machines Compute the Uncomputable? Minds and Machines 21 (2):221-239.score: 2.0
  27. B. Jack Copeland (2002). Accelerating Turing Machines. Minds and Machines 12 (2):281-300.score: 2.0
    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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  28. Bruno Scarpellini (2003). Comments on `Two Undecidable Problems of Analysis'. Minds and Machines 13 (1):79-85.score: 2.0
    We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is (...)
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  29. Taner Edis & Maarten Boudry (forthcoming). Beyond Physics? On the Prospects of Finding a Meaningful Oracle. Foundations of Science:1-20.score: 2.0
    Certain enterprises at the fringes of science, such as intelligent design creationism, claim to identify phenomena that go beyond not just our present physics but any possible physical explanation. Asking what it would take for such a claim to succeed, we introduce a version of physicalism that formulates the proposition that all available data sets are best explained by combinations of “chance and necessity”—algorithmic rules and randomness. Physicalism would then be violated by the existence of oracles that produce certain kinds (...)
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  30. Tim Button (2009). Hyperloops Do Not Threaten the Notion of an Effective Procedure. Lecture Notes in Computer Science 5635:68-78.score: 2.0
    This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.
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  31. Merlin Carl, Tim Fischbach, Peter Koepke, Russell Miller, Miriam Nasfi & Gregor Weckbecker (2010). The Basic Theory of Infinite Time Register Machines. Archive for Mathematical Logic 49 (2):249-273.score: 2.0
    Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is set (...)
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  32. Peter Koepke & Ryan Siders (2008). Register Computations on Ordinals. Archive for Mathematical Logic 47 (6):529-548.score: 2.0
    We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register (...)
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  33. Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.score: 1.0
    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 Effective version (...)
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  34. Yoel Matveyev (2011). Between Enlightenment and Romanticism: Computational Kabbalah of Rabbi Pinchas Elijah Hurwitz. History and Philosophy of Logic 32 (1):85-101.score: 1.0
    This article shows that Rabbi Pinchas Elijah Hurwitz, a major eighteenth-century kabbalist, Orthodox rabbi and Enlightenment thinker, who merged Lurianic Kabbalah with Kantian philosophy, attempted to describe God and the world in terms of formal grammars and abstract information processes. He resolves a number of Kant's dualistic views by introducing prophecy as a tool that allows a mystic's mind to perform transfinite hypercomputation and to obtain a priori knowledge about things usually known only a posteriori. According to Hurwitz, the reality (...)
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  35. Selmer Bringsjord, In Defense of the Unprovability of the Church-Turing Thesis.score: 1.0
    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 necessary preliminaries (...)
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  36. Andrew Hodges, Alan Turing in the Stanford Encyclopedia of Philosophy.score: 1.0
    The origin of my article lies in the appearance of Copeland and Proudfoot's feature article in Scientific American, April 1999. This preposterous paper, as described on another page, suggested that Turing was the prophet of 'hypercomputation'. In their references, the authors listed Copeland's entry on 'The Church-Turing thesis' in the Stanford Encyclopedia. In the summer of 1999, I circulated an open letter criticising the Scientific American article. I included criticism of this Encyclopedia entry. This was forwarded (by Prof. Sol Feferman) (...)
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