Results for 'hypercomputation'

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  1. 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 thesis.
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  2. Hypercomputation.B. Jack Copeland - 2002 - Minds and Machines 12 (4):461-502.
  3. Quantum Hypercomputability?Amit Hagar & Alexandre Korolev - 2006 - Minds and Machines 16 (1):87-93.
    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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  4. 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 yields that the (...)
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  5. Quantum Hypercomputation.Tien D. Kieu - 2002 - Minds and Machines 12 (4):541-561.
    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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  6.  57
    Hypercomputation: Computing More Than the Turing Machine.Toby Ord - 2002 - Dissertation, University of Melbourne
    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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  7. Quantum Hypercomputation—Hype or Computation?Amit Hagar & Alex Korolev - 2007 - Philosophy of Science 74 (3):347-363.
    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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  8.  7
    Biological Hypercomputation: A New Research Problem in Complexity Theory.Carlos E. Maldonado & Nelson A. Gómez Cruz - 2015 - Complexity 20 (4):8-18.
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  9. 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 are specified such (...)
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  10. Computation and Hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.
    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 (...)
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  11.  8
    Computation, Hypercomputation, and Physical Science.Konstantine Arkoudas - 2008 - Journal of Applied Logic 6 (4):461-475.
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  12. The Diagonal Method and Hypercomputation.Toby Ord & Tien D. Kieu - 2005 - British Journal for the Philosophy of Science 56 (1):147-156.
    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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  13.  41
    The Many Forms of Hypercomputation.Toby Ord - unknown - Journal of Applied Mathematics and Computation 178:142-153.
    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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  14.  82
    Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW]Aran Nayebi - 2014 - Minds and Machines 24 (3):275-305.
    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 (...)
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  15.  1
    Superminds: People Harness Hypercomputation, and More.Mark Phillips, Selmer Bringsjord & M. Zenzen - 2003 - Dordrecht, Netherland: Springer Science & Business Media.
    When Ken Malone investigates a case of something causing mental static across the United States, he is teleported to a world that doesn't exist.
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  16. A Brief Critique of Pure Hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.
    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 (...)
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  17.  56
    The Modal Argument for Hypercomputing Minds.Selmer Bringsjord - 2004 - Theoretical Computer Science 317.
  18.  27
    On the Possibility, or Otherwise, of Hypercomputation.Philip D. Welch - 2004 - British Journal for the Philosophy of Science 55 (4):739-746.
    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 (...)
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  19. Toward a Formal Philosophy of Hypercomputation.Selmer Bringsjord & Michael Zenzen - 2002 - Minds and Machines 12 (2):241-258.
    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 (...)
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  20.  24
    Learning to Hypercompute? An Analysis of Siegelmann Networks.Keith Douglas - 2013 - In Gordana Dodig-Crnkovic Raffaela Giovagnoli (ed.), Computing Nature. pp. 201--211.
  21.  36
    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]E. Mendelson - 2005 - Philosophia Mathematica 13 (2):228-230.
  22.  4
    Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity.Péter Németi & Gergely Székely - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 528--538.
  23.  5
    Something Old, Something New, Something Borrowed, Something Blue Part 1: Alan Turing, Hypercomputation, Adam Smith and Next Generation Intelligent Systems.Mark Dougherty - 2012 - Journal of Intelligent Systems 21 (4):325-330.
    . In this article intelligent systems are placed in the context of accelerated Turing machines. Although such machines are not currently a reality, the very real gains in computing power made over previous decades require us to continually reevaluate the potential of intelligent systems. The economic theories of Adam Smith provide us with a useful insight into this question.
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  24. Do Accelerating Turing Machines Compute the Uncomputable?B. Jack Copeland & Oron Shagrir - 2011 - Minds and Machines 21 (2):221-239.
    Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as “the work-horse of hypercomputation”. But do they really compute beyond the “Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term “accelerating Turing machine” is (...)
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  25.  97
    On Effective Procedures.Carol E. Cleland - 2002 - Minds and Machines 12 (2):159-179.
    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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  26.  18
    Buttresses of the Turing Barrier.Paolo Cotogno - 2015 - Acta Analytica 30 (3):275-282.
    The ‘Turing barrier’ is an evocative image for 0′, the degree of the unsolvability of the halting problem for Turing machines—equivalently, of the undecidability of Peano Arithmetic. The ‘barrier’ metaphor conveys the idea that effective computability is impaired by restrictions that could be removed by infinite methods. Assuming that the undecidability of PA is essentially depending on the finite nature of its computational means, decidability would be restored by the ω-rule. Hypercomputation, the hypothetical realization of infinitary machines through relativistic (...)
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  27.  19
    Constructibility of the Universal Wave Function.Arkady Bolotin - 2016 - Foundations of Physics 46 (10):1253-1268.
    This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over the meaning of the wave function of the universe. As it is demonstrated in the paper, unless the number of the universe’s degrees of freedom is fundamentally upper bounded or hypercomputation is physically realizable, the universal wave function is a non-constructive entity in the sense of constructive (...)
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  28.  75
    What Turing Did After He Invented the Universal Turing Machine.Diane Proudfoot & Jack Copeland - 2000 - Journal of Logic, Language and Information 9:491-509.
    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 (...)
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  29. Significance of Models of Computation, From Turing Model to Natural Computation.Gordana Dodig-Crnkovic - 2011 - Minds and Machines 21 (2):301-322.
    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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  30. 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 Effective (...)
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  31.  38
    Register Computations on Ordinals.Peter Koepke & Ryan Siders - 2008 - Archive for Mathematical Logic 47 (6):529-548.
    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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  32. Hyperloops Do Not Threaten the Notion of an Effective Procedure.Tim Button - 2009 - Lecture Notes in Computer Science 5635:68-78.
    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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  33.  69
    The Basic Theory of Infinite Time Register Machines.Merlin Carl, Tim Fischbach, Peter Koepke, Russell Miller, Miriam Nasfi & Gregor Weckbecker - 2010 - Archive for Mathematical Logic 49 (2):249-273.
    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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  34.  37
    Comments on `Two Undecidable Problems of Analysis'.Bruno Scarpellini - 2003 - Minds and Machines 13 (1):79-85.
    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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  35.  16
    Philosophical Issues About Black Holes.Gustavo E. Romero - unknown
    Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermadynamics and (...)
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  36.  64
    Alan Turing in the Stanford Encyclopedia of Philosophy.Andrew Hodges - unknown
    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 to Prof. Ed (...)
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  37.  51
    Between Enlightenment and Romanticism: Computational Kabbalah of Rabbi Pinchas Elijah Hurwitz.Yoel Matveyev - 2011 - History and Philosophy of Logic 32 (1):85-101.
    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 (...)
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  38.  1
    The Significance of Relativistic Computation for the Philosophy of Mathematics.Krzysztof Wójtowicz - 2021 - In Elena Aladova, Pablo Barceló, Johan van Benthem, Gerald Berger, Katrin M. Dannert, Neil Dewar, Răzvan Diaconescu, Ivo Düntsch, Wojciech Dzik, M. Eyad Kurd-Misto, Giambattista Formica, Michèle Friend, Robert Goldblatt, Georg Gottlob, Erich Grädel, Robin Hirsch, Ian Hodkinson, Marcel Jackson, Peter Jipsen, Roger D. Maddux, J. B. Manchak, Ewa Orłowska, Andreas Pieris, Boris Plotkin, Tatjana Plotkin, Vaughan R. Pratt, Ian Pratt-Hartmann, Tarek Sayed Ahmed, James Owen Weatherall, Dag Westerståhl, James Wimberley, Krzysztof Wójtowicz & Christian Wüthrich (eds.), Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic. Springer Verlag. pp. 165-183.
    In the paper I discuss the importance of relativistic hypercomputation for the philosophy of mathematics, in particular for our understanding of mathematical knowledge. I also discuss the problem of the explanatory role of mathematics in physics and argue that relativistic computation fits very well into the so-called programming account. Relativistic computation reveals an interesting interplay between the empirical realm and the realm of very abstract mathematical principles that even exceed standard mathematics and suggests, that such principles might play an (...)
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  39. Is There Any Real Substance to the Claims for a 'New Computationalism'?Alberto Hernandez-Espinosa, Hernandez-Quiroz Francisco & Zenil Hector - forthcoming - In CiE Computability in Europe 2017. Springer Verlag.
    'Computationalism' is a relatively vague term used to describe attempts to apply Turing's model of computation to phenomena outside its original purview: in modelling the human mind, in physics, mathematics, etc. Early versions of computationalism faced strong objections from many (and varied) quarters, from philosophers to practitioners of the aforementioned disciplines. Here we will not address the fundamental question of whether computational models are appropriate for describing some or all of the wide range of processes that they have been applied (...)
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  40.  67
    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 necessary (...)
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  41. 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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  42.  16
    Positive affirmation of non-algorithmic information processing.Carlos Eduardo Maldonado - 2017 - Cinta de Moebio 60:279-285.
    : One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Biological hypercomputation is the concept coined that expresses that living beings process information non-algorithmically. This paper aims at proving a positive understanding of “non-algorithmic” processes. Many arguments are brought that support the claim. This (...)
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  43.  12
    O różnych sposobach rozumienia analogowości w informatyce.Paweł Stacewicz - 2017 - Semina Scientiarum 16:94-115.
    Two different types of analog computations are discussed in the paper: 1) analog-continuous computations, 2) analog-analogical computations. They are analyzed with regard to such questions like: a) are continuous computations physically implementable? b) what is the actual computational power of different analog techniques? c) can natural computations be such reliable as digital? d) is it possible to develop universal analog computers? Presented analyses are rather methodological than formal.
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  44.  4
    Is Church’s Thesis Still Relevant?Jerzy Mycka & Adam Olszewski - 2020 - Studies in Logic, Grammar and Rhetoric 63 (1):31-51.
    The article analyses the role of Church’s Thesis in the context of the development of hypercomputation research. The text begins by presenting various views on the essence of computer science and the limitations of its methods. Then CT and its importance in determining the limits of methods used by computer science is presented. Basing on the above explanations, the work goes on to characterize various proposals of hypercomputation showing their relative power in relation to the arithmetic hierarchy. The (...)
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  45. 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. We (...)
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  46.  41
    Beyond Physics? On the Prospects of Finding a Meaningful Oracle.Taner Edis & Maarten Boudry - 2014 - Foundations of Science 19 (4):403-422.
    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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