Notes:

Hypercomputation is a field of study that focuses on the development of computing systems that are capable of performing computations that are beyond the capabilities of conventional computers. This includes computations that are considered to be non-computable or unsolvable by conventional means, such as the halting problem or the busy beaver function.

While there have been many proposed designs for hypercomputers, in their current form, these systems are far from being practical. This is because the development of hypercomputation is a highly challenging and complex field, and there are many technical and theoretical obstacles that must be overcome in order to build a functional hypercomputer.

In addition, there are many skeptics who argue that the concept of hypercomputation is flawed, and that it is impossible to build a machine that can perform non-computable or unsolvable computations. These skeptics argue that the limitations of computation are fundamental and cannot be overcome, and that the pursuit of hypercomputation is a misguided or pseudoscientific endeavor.

Resources:

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AIML & Ontologies | AIML Templates

**Three counterexamples refuting Kieu’s plan for “quantum adiabatic hypercomputation”; and some uncomputable quantum mechanical tasks** WD Smith – Applied Mathematics and Computation, 2006 – Elsevier Tien D. Kieu, in 10 papers posted to the quant-ph section of the xxx. lanl. gov preprint archive [some of which were also published in printed journals such as Proc. Royal Soc. A 460 (2004) 1535] had claimed to have a scheme showing how, in principle, physical “ … Cited by 37 Related articles All 9 versions

**The many forms of hypercomputation** T Ord – Applied mathematics and computation, 2006 – Elsevier The Turing machine was developed as a formalisation of the concept of computation. While algorithms had played key roles in certain areas of mathematics, prior to the 1930s they had not been studied as mathematical entities in their own right. Alan Turing [41] changed this by introducing a … Cited by 48 Related articles All 12 versions

[BOOK] **Hypercomputation: computing beyond the Church-Turing barrier** A Syropoulos – 2008 – books.google.com Hypercomputation is a relatively new theory of computation that is about computing methods and devices that transcend the so-called Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation covering all attempts at devising … Cited by 56 Related articles All 8 versions

**The case for hypercomputation** M Stannett – Applied Mathematics and Computation, 2006 – Elsevier The weight of evidence supporting the case for hypercomputation is compelling. We examine some 20 physical and mathematical models of computation that are either known or suspected to have super-Turing or hypercomputational capabilities, and argue that … Cited by 40 Related articles All 6 versions

**The diagonal method and hypercomputation** T Ord, TD Kieu – The British journal for the philosophy of …, 2005 – Br Soc Philosophy Sci Abstract 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 … Cited by 34 Related articles All 15 versions

**Zeno machines and hypercomputation** PH Potgieter – Theoretical Computer Science, 2006 – Elsevier This paper reviews the Church–Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of “hypercomputation”, concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with … Cited by 25 Related articles All 10 versions

**Real hypercomputation and continuity** M Ziegler – Theory of Computing Systems, 2007 – Springer Abstract By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of hypercomputation allow for the effective evaluation of also discontinuous f:{\BbbR?\BbbR … Cited by 29 Related articles All 14 versions

**Non-classical hypercomputation** SSNC Hypercomputation – Int. J. Unconventional …, 2009 – www-users.cs.york.ac.uk Hypercomputation that seeks to solve the Halting Problem, or to compute Turing- uncomputable numbers, might be called “classical” hypercomputation, as it moves beyond the classical Turing computational paradigm. There are further computational paradigms … Cited by 5 Related articles All 9 versions

**Five Views of Hypercomputation**. B Loff, JF Costa – IJUC, 2009 – math.ist.utl.pt In (7; 8) Martin Davis criticises the relevance of so-called hypercomputation. Is hypercomputation a new theory to help us understand the mathematics of hyperdegrees, or is it a theory about concrete computation in the physical world? We review the concept of … Cited by 12 Related articles All 13 versions

**Quantum Hypercomputation—Hype or Computation?*** A Hagar, A Korolev – Philosophy of Science, 2007 – JSTOR 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 ( … Cited by 12 Related articles All 7 versions

**Physical constraints on hypercomputation** P Cockshott, L Mackenzie, G Michaelson – Theoretical Computer Science, 2008 – Elsevier Many attempts to transcend the fundamental limitations to computability implied by the Halting Problem for Turing Machines depend on the use of forms of hypercomputation that draw on notions of infinite or continuous, as opposed to bounded or discrete, computation. … Cited by 9 Related articles All 7 versions

**Beyond turing: hypercomputation and quantum morphogenesis** I Licata – Asia Pacific Mathematics Newsletter, 2012 – asiapacific-mathnews.com We note, in particular, that the first point refers to a generic discrete structure of the world, but contains no specific information on the proper dynamics of quantum processes, and point (b) is connected to a locality principle. Finally, point (c) stresses the universality of the Turing … Cited by 11 Related articles All 3 versions

**Hypercomputation, unconsciousness and entertainment technology** M Rauterberg – Fun and Games, 2008 – Springer Abstract Recent developments in computer science introduce and discuss new concepts for computation beyond universal Turing machines. Quantum computing relates to new insights in quantum physics as interference and entanglement based on nonlocality. Several ideas … Cited by 8 Related articles All 9 versions

**Super-Turing or non-Turing? Extending the concept of computation** BJ MacLennan – International Journal of Unconventional Computing, 2009 – cs.utk.edu “Hypercomputation” is often defined as transcending Turing computation in the sense of computing a larger class of functions than can Turing machines. While this possibility is important and interesting, this paper argues that there are many other important senses in … Cited by 15 Related articles All 13 versions

**Existence of faster than light signals implies hypercomputation already in special relativity** P Németi, G Székely – How the World Computes, 2012 – Springer Abstract Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals. Cited by 7 Related articles All 10 versions

**Evolving recurrent neural networks are super-turing** J Cabessa, HT Siegelmann – Neural Networks (IJCNN), The …, 2011 – ieeexplore.ieee.org Abstract—The computational power of recurrent neural networks is intimately related to the nature of their synaptic weights. In particular, neural networks with static rational weights are known to be Turing equivalent, and recurrent networks with static real weights were … Cited by 12 Related articles All 2 versions

**How much can analog and hybrid systems be proved (super-) Turing** O Bournez – Applied Mathematics and Computation, 2006 – Elsevier Church thesis and its variants say roughly that all reasonable models of computation do not have more power than Turing machines. In a contrapositive way, they say that any model with super-Turing power must have something unreasonable. Our aim is to discuss how … Cited by 12 Related articles All 14 versions

**Real computability and hypercomputation** M Ziegler – 2007 – cs.uni-paderborn.de Summary: Turing machines are generally agreed to be the appropriate mathematical idealization describing the capabilities of actual digital computers. With regard to computations on real numbers (being continuous rather than digital objects), two major … Cited by 7 Related articles

**How to acknowledge hypercomputation?** A Leitsch, G Schachner, K Svozil – 2007 – Citeseer It is widely acknowledged [1, 2] that every physical system corresponds to a com- putational process, and that every computational process, if applicable, has to be physically and operationally feasible in some concrete realization. In this sense, the physical and computational … Cited by 5 Related articles All 11 versions

**(Short) Survey of Real Hypercomputation** M Ziegler – Computation and Logic in the Real World, 2007 – Springer Any theory of computability must rely on some model of computation, that is a mathematical abstraction and idealization of the kind of actual devices whose fundamental power the theory is to describe. On the discrete realm several major such notions of effectivity (Turing machines, … Cited by 5 Related articles All 3 versions

**The Myth of ‘The Myth of Hypercomputation’** NS Govindarajulu, S Bringsjord – Parallel Processing Letters, 2012 – World Scientific A myth has unfortunately arisen in connection with Martin Davis’s rather aggressively titled paper” The Myth of Hypercomputation.” The myth is that Davis is profoundly and decisively right therein, and that hypercomputation is indeed therefore a myth. We show herein that … Cited by 4 Related articles

**Constraints on hypercomputation** G Michaelson, P Cockshott – Logical Approaches to Computational …, 2006 – Springer Abstract Wegner and Eberbach [16] have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so- called superTuring models. In this paper we contest their claims for interaction machines … Cited by 4 Related articles All 12 versions

**Some thoughts on hypercomputation** NCA da Costa, FA Doria – Applied mathematics and computation, 2006 – Elsevier We first show that the Halting Function (the noncomputable function that solves the Halting Problem) has explicit expressions in the language of calculus. Out of that fact we elaborate on the possible meaning of hypercomputation theory within the setting of formal … Cited by 4 Related articles All 9 versions

**Biological hypercomputation: A new research problem in complexity theory** CE Maldonado, G Cruz, A Nelson – Complexity, 2014 – Wiley Online Library This article discusses the meaning and scope of biological hypercomputation (BH) that is to be considered as new research problem within the sciences of complexity. The framework here is computational, setting out that life is not a standard Turing Machine. Living systems … Cited by 4 Related articles All 2 versions

**New physics and hypercomputation** I Németi, H Andreka – SOFSEM, 2006 – cs.cas.cz Abstract. Does new physics give us a chance for designing computers, at least in principle, which could compute beyond the Turing barrier? By the latter we mean computers which could compute some functions which are not Turing computable. Part of what we call “new … Cited by 4 Related articles All 14 versions

**The super-turing computational power of interactive evolving recurrent neural networks** J Cabessa, AEP Villa – Artificial Neural Networks and Machine Learning– …, 2013 – Springer Abstract Understanding the dynamical and computational capabilities of neural models represents an issue of central importance. Here, we consider a model of first-order recurrent neural networks provided with the possibility to evolve over time and involved in a basic … Cited by 5 Related articles All 4 versions

**Interactive Evolving Recurrent Neural Networks Are Super-turing**. J Cabessa – ICAART (1), 2012 – jcabessa.byethost32.com Abstract: We consider a model of evolving recurrent neural networks where the synaptic weights can change over time, and we study the computational power of such networks in a basic context of interactive computation. In this framework, we prove that both models of … Cited by 5 Related articles

**Quantum algorithm of hypercomputation based on the Poschl-Teller potential** M Vélez, A Sicard, J Ospina – Revista Colombiana de Física, 2006 – eafit.edu.co ABSTRACT We constructed an hypercomputational quantum algorithm based on Pöschl- Teller potentials, Lie algebra su (1, 1), and an adiabatic evolution. Our algorithm resolves in principle Hilbert’s tenth problem, a classically non-computable problem. Our algorithm is … Cited by 3 Related articles All 6 versions

**Membrane systems and hypercomputation** M Stannett – Membrane Computing, 2013 – Springer Abstract We present a brief analysis of hypercomputation and its relationship to membrane systems theory, including a re-evaluation of Turing’s analysis of computation and the importance of timing structure, and suggest a ‘cosmological’variant of tissue P systems that … Cited by 3 Related articles All 3 versions

**Computation, hypercomputation, and physical science** K Arkoudas – Journal of Applied Logic, 2008 – Elsevier Copeland and others have argued that the Church–Turing thesis (CTT) has been widely misunderstood by philosophers and cognitive scientists. In particular, they have claimed that CTT is in principle compatible with the existence of machines that compute functions … Cited by 3 Related articles All 3 versions

**Membrane system models for super-Turing paradigms** M Gheorghe, M Stannett – Natural Computing, 2012 – Springer Abstract We extend Calude and P?un’s accelerating P system model of computation, and investigate the computational power of the resulting systems. We show that the resulting systems can solve problems at all levels of the arithmetical hierarchy, and that the higher … Cited by 4 Related articles All 7 versions

**Beyond the super-turing snare: analog computation and digital virtuality** G Trautteur – New Computational Paradigms, 2005 – Springer Abstract Conceptual difficulties involved in attempts to build analog super-Turing sources are examined in the light of epistemic problems of physical measurement. Basic concepts of computability theory are appealed to in order to set up a procedural comparison between … Cited by 4 Related articles All 6 versions

**Turing on super-Turing and adaptivity** HT Siegelmann – Progress in biophysics and molecular biology, 2013 – Elsevier Abstract Biological processes are often compared to computation and modeled on the Universal Turing Machine. While many systems or aspects of systems can be well described in this manner, Turing computation can only compute what it has been programmed for. It … Cited by 4 Related articles All 6 versions

**Industrial Hypercomputation** M Stannett – The Grand Challenge in Non-Classical Computation …, 2005 – cs.york.ac.uk Hypercomputation is the study of real or theoretical systems which display ‘super- Turing’potential, systems that can do provably more than today’s machines. The study of these systems is truly interdisciplinary, involving fields as diverse as computer science [13] … Cited by 2 Related articles All 2 versions

**From hypocomputation to hypercomputation** D Love – 2008 – Citeseer Abstract Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have been lost. So … Cited by 2 Related articles All 6 versions

**A brief critique of pure hypercomputation** P Cotogno – Minds and Machines, 2009 – Springer Abstract 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 … Cited by 3 Related articles All 8 versions

**Quantum hypercomputation based on the dynamical algebra\ mathfrak {su}(1\ hbox {,} 1)** A Sicard, J Ospina, M Vélez – Journal of Physics A: Mathematical …, 2006 – iopscience.iop.org Abstract An adaptation of Kieu’s hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl–Heisenberg algebra by other dynamical algebra of low dimension that admits infinitedimensional irreducible … Cited by 2 Related articles All 10 versions

**Using Isabelle to verify special relativity, with application to hypercomputation theory** M Stannett, I Németi – arXiv preprint arXiv:1211.6468, 2012 – arxiv.org Abstract: Logicians at the R\’enyi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first order logic, and have argued in favour of the physical decidability, via … Cited by 2 Related articles All 5 versions

**Practical intractability: A critique of the hypercomputation movement** A Nayebi – Minds and Machines, 2014 – Springer Abstract 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 … Cited by 2 Related articles All 6 versions

**Possibility of Hypercomputation from the Standpoint of Superluminal Particles** T Musha – Theory and Applications of Mathematics & Computer …, 2013 – uav.ro Abstract In mathematics and computer science, an accelerated Turing machine is a hypothetical computational model related to Turing machines, which can perform the countable infinite number of computational steps within a finite time. But this machine … Cited by 1 Related articles All 4 versions

**Something Old, Something New, Something Borrowed, Something Blue Part 1: Alan Turing, Hypercomputation, Adam Smith and Next Generation Intelligent Systems** M Dougherty – 2012 – degruyter.com Abstract. 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 … Cited by 1 Related articles All 2 versions

**Small steps toward hypercomputation via infinitary machine proof verification and proof generation** NS Govindarajulu, J Licato, S Bringsjord – … Computation and Natural …, 2013 – Springer Abstract After setting a context based on two general points (that humans appear to reason in infinitary fashion, and two, that actual hypercomputers aren’t currently available to directly model and replicate such infinitary reasoning), we set a humble engineering goal of taking … Cited by 1 Related articles All 3 versions

**Some thoughts on hypercomputation** A Syropoulos – arXiv preprint arXiv:0910.1494, 2009 – arxiv.org Abstract: Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church–Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its apparent … Cited by 1 Related articles All 4 versions

**Physical hypercomputation** M Stannett – A. Adamatzky, L. Bull, B. De Lacy Costello, S. …, 2007 – books.google.com Abstract We argue that observable values and the physical systems that generate them need not have representations belonging to the same computational class. It is possible both for computable systems to generate uncomputable values, and also for … Cited by 1 Related articles

**Development of Physical Super-Turing Analog Hardware** AS Younger, E Redd, H Siegelmann – Unconventional Computation and …, 2014 – Springer Abstract In the 1930s, mathematician Alan Turing proposed a mathematical model of computation now called a Turing Machine to describe how people follow repetitive procedures given to them in order to come up with final calculation result. This … Cited by 1 Related articles

**General Intelligence and Hypercomputation** S Bringsjord – Artificial General Intelligence, 2009 – books.google.com From its revolutionary arrival on the behaviorismdominated scene, the information- processing approach to both understanding human intelligence, and to the attempt to bestow such intelligence on a machine, has always proceeded under the assumption that … Related articles All 8 versions

**Hypercomputation: Fantasy Or Reality? A Position Paper** A Syropoulos – Parallel Processing Letters, 2013 – World Scientific Hypercomputation is about the feasibility of machines and systems that are either more expressive or computationally more powerful than the Turing machine. A number of researchers and thinkers have put forth a number of supposedly knock-out arguments … Related articles

**Physical Constraints on Hypercomputation** PCLMG Michaelsonc – qucis.queensu.ca Many attempts to transcend the fundamental limitations to computability implied by the Halting Problem for Turing Machines depend on the use of forms of hypercomputation that draw on notions of infinite or continuous, as opposed to bounded or discrete, computation. … Related articles All 3 versions

**Hypercomputation and the Grand Challenge in Non-Classical Computation** S Stepney – 2006 – cs.york.ac.uk Page 1. hypercomputation — 1 Department of Computer Science Hypercomputation and the Grand Challenge in … hypercomputation — 24 Department of Computer Science environmental hypercomputation • wanted: a computational paradigm that naturally includes – noise … Related articles All 7 versions

**Decidability of Arithmetic Through Hypercomputation: Logical Objections** P Cotogno – 12345efghi – cs.swan.ac.uk Abstract. The theory of hypercomputation aims to extend effective computability beyond Turing reducibility, in particular by means of supertasks; physical models are considered in Newtonian, relativistic and quantum contexts. Apart from implementation differences, all … Cited by 1 Related articles All 5 versions

**Hypercomputation: Towards an extension of the classical notion of Computability**? G Kasa – arXiv preprint arXiv:1210.7171, 2012 – arxiv.org Abstract: The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical Computability with … Related articles All 2 versions

**Real Hypercomputation and Degrees of Discontinuity** M Ziegler – arXiv preprint cs/0607114, 2006 – Citeseer Abstract. By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS 2000), Brattka (MLQ 2005), and Ziegler (ToCS2006) have considered different relaxed notions of … Related articles All 3 versions

**Hypercomputation in a Cryptographic Setting: Solving the Identity Theft Problem Using Quantum Memorie**s? N Nagy, M Nagy, SG Akl – IJUC, 2010 – oldcitypublishing.com The identity theft problem, an ever growing threat to safety and security in today’s society, is very difficult to tackle using classical means, due to the fact that classical information can be easily read and copied. In this paper, we show that we can do more than it is possible … Related articles All 4 versions

**HyperTrends’ 06: International Multidisciplinary Workshop on Future Trends in Hypercomputation Sheffield, 11-13 September 2006** M Stannett – 2006 – hypercomputation.net Abstract: Although hypercomputation is a “tabu” subject, researchers are not united when they present their own ideas of what computing above Turing means. In this talk I will prove that five different cliques are emerging and that they do not agree with each other; that … Related articles

**proceedings of the 4th International Workshop on Physics and Computation (P&C 2011) and the 3rd International Hypercomputation Workshop (HyperNet 11) …** M Stannett – 2011 – hypercomputation.net Abstract We present a counterexample to Krasnikov’s (2002) much discussed time machine no-go result. In addition, we prove a positive statement: a time machine existence theorem under a modest “no holes” assumption. Key words: Time Machines, Time Travel, Causality … Related articles All 5 versions

**On Super-Turing Neural Computation** J Cabessa, AEP Villa – Advances in Cognitive Neurodynamics (IV), 2015 – Springer Abstract In this paper, we provide a historical survey of the most significant results concerning the computational power of neural models. We distinguish three important periods: first, the early works from McCulloch and Pitts, Kleene, and Minky, where the … Related articles All 3 versions

**Quantum Vacuum Dynamics, Coherence, Superluminal Photons and Hypercomputation in Brain Microtubules** LM Caligiuri, T Musha – europment.org Abstract—Recent researches have shown the theoretical possibility of accomplishing hypercomputation in human brain by using eventual superluminal evanescent photons generated inside brain’s microtubules, using these as quantum waveguides or resonant … Related articles All 3 versions

**Future Trends in Hypercomputation** M Stannett – 2009 – cs.swansea.ac.uk Turing wanted to model the way mathematicians behave when they prove things; his “machine” simulates the way we make notes, do calculations on scraps of paper, and so on. The result is a general representation of ‘algorithmic mathematical behaviour’–the sort of … All 5 versions

**Might the Rigorous Modeling of Economic Phenomena Require Hypercomputation?** S Bringsjord, E Eberbach, Y Yang – 2010 – cs.rpi.edu Mathematical logic was born from the rigorous formalization and study of mathematics using computation and formal logic, and includes such seminal results as Gödel’s incompleteness theorems and Turing’s halting-problem result, proved at the dawn of computer science. … Related articles

**Why is it necessary to build a physical model of hypercomputation?** F Franchette – Proceedings of AISB’11: Computing and …, 2011 – hal.archives-ouvertes.fr A model of hypercomputation can compute at least one function not computable by Turing Machine and its power comes from the absence of particular restrictions on the computation. Nowadays, some researchers claim that it is possible to build a physical model of … All 3 versions

**Physical Constraints on Hypercomputation** EH Riccarton – dcs.gla.ac.uk Abstract” To infinity, and beyond!”, Buzz Lightyear, Toy Story, Pixar, 1995. Many attempts to transcend the fundamental limitations to computability implied by the Halting Problem for Turing Machines depend on the use of forms of hypercomputation that draw on notions of … Related articles All 5 versions

**Biological Hypercomputation: A Concept is Introduced** CE Maldonado, NA Gómez-Cruz – arXiv preprint arXiv:1210.4819, 2012 – arxiv.org Abstract: This paper discusses the meaning and scope of biological hypercomputation (BH). The framework here is computational, and from the outset it should be clear that life is not a standard Turing Machine. Living systems hypercompute, but the distinction is made … Related articles All 6 versions

**A Hypercomputation in Brouwer’s Constructivism** R Ramezanian – arXiv preprint arXiv:1408.2930, 2014 – arxiv.org Abstract: In contrast to other constructivist schools, for Brouwer, the notion of” constructive object” is not restricted to be presented aswords’ in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate … Related articles All 2 versions

**Selmer Bringsjord and Michael Zenzen. Superminds: People Harness Hypercomputation, and More**. Studies in Cognitive Systems, Volume 29. Dordrecht: Kluwer … E Mendelson – Philosophia Mathematica, 2005 – Oxford Univ Press This is not science fiction about minds or machines that have powers that exceed those of ordinary men and women. Nor is it a study of people with exceptionally bright intellects. Rather, it is principally a broadside aimed at refuting what the authors call … All 3 versions

[BOOK] **Models of hypercomputation** E Acar – 2012 – Citeseer Abstract After presenting preliminary knowledge in Computability Theory, some versions and interpretations of the so called Church-Turing thesis will be discussed. A mathematical definition of hypercomputation will be given. Some proposed abstract and physical … Related articles All 6 versions

**Real Hypercomputation with Infinite Oracle Queries** A Pauly – Mathematical Theory and Computational Practice – math.uni-heidelberg.de We define Oracle-Type-2-Machine capable of writing infinite oracle queries. In contrast to finite oracle queries, this extends the realm of oracle-computable function into the discontinuous realm. Our definition is conservative; access to a computable oracle does … Related articles All 5 versions

**Guest Editor’S Note: Special Issue On Hypercomputation, Physics And Computation** M Stannett – Parallel Processing Letters, 2012 – World Scientific In the little more than a decade since the term was first coined by Copeland and Proudfoot [1], hypercomputation theory (the study of physical and/or logical systems capable of non- Turing-simulable behaviours) has advanced and widened considerably, especially in … Related articles

**Theory, Evolution of Space-time, Mind And Complex Systems, Quantum Entanglement, Cold Atoms, Intermolecular Interactions, Hypercomputation Already Extant And …** KNP Kumar, BS Kiranagi, G Prabhu – Advances in Physics Theories and …, 2012 – iiste.org Abstract Quantum Computation, Neurobiology, Subjective Vision, Human Medial Temporal Lobe, Consciousness, Unconsciousness, Conscious Vision, schizophrenia, Quantum Holography, Neurocomputer Architectures, Heisenberg Theory, Molecular Computation, … All 2 versions

**Natural Computation and Hypercomputation** A Syropoulos – Hypercomputation: Computing Beyond the Church- …, 2008 – Springer Hypercomputation is not only about the falsification of the Church–Turing thesis, but also about the broadening of the concept of computation. This implies that the Turing machine model of computation, which is based on a small number of assumptions, cannot and …

**On Super-Turing Computing Power and Hierarchies of Artificial General Intelligence Systems** J Wiedermann – Artificial General Intelligence, 2010 – Citeseer Abstract Using the contemporary view of computing exemplified by recent models and results from non-uniform complexity theory we investigate the computational power of artificial general intelligence systems (AGISs). We show that in accordance with the so- … Related articles All 5 versions

**The Super-Turing Computational Power of Plastic Recurrent Neural Networks** J Cabessa, HT Siegelmann – International journal of neural systems, 2014 – World Scientific We study the computational capabilities of a biologically inspired neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve over time rather than stay static. Our study focuses on the mere concept of plasticity of the model so … Related articles All 6 versions

**Relativistic and Quantum Hypercomputation** A Syropoulos – Hypercomputation: Computing Beyond the Church- …, 2008 – Springer The theory of infinite-time Turing machines is practically useless unless it is possible to perform a supertask. If we can find ways to perform supertasks, we have in our hands a real tool to study a particular form of hypercomputation. In this chapter, I present a number of …

**Recurrent Neural Networks and Super-Turing Interactive Computation** J Cabessa, AEP Villa – Artificial Neural Networks, 2015 – Springer Abstract We present a complete overview of the computational power of recurrent neural networks involved in an interactive bio-inspired computational paradigm. More precisely, we recall the results stating that interactive rational-and realweighted neural networks are … Related articles All 3 versions

**Interactive Evolving Recurrent Neural Networks Are Super-Turing Universal** J Cabessa, AEP Villa – Artificial Neural Networks and Machine Learning– …, 2014 – Springer Abstract Understanding the dynamical and computational capabilities of neural models represents an issue of central importance. In this context, recent results show that interactive evolving recurrent neural networks are super-Turing, irrespective of whether their synaptic … Related articles All 3 versions