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Journal articles on the topic 'Machine de turing'

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Published: 5 October 2024

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1

Daylight, Edgar Graham. "Refining Mark Burgin’s Case against the Church–Turing Thesis." Philosophies 9, no. 4 (August 12, 2024): 122. http://dx.doi.org/10.3390/philosophies9040122.

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The outputs of a Turing machine are not revealed for inputs on which the machine fails to halt. Why is an observer not allowed to see the generated output symbols as the machine operates? Building on the pioneering work of Mark Burgin, we introduce an extension of the Turing machine model with a visible output tape. As a subtle refinement to Burgin’s theory, we stipulate that the outputted symbols cannot be overwritten: at step i, the content of the output tape is a prefix of the content at step j, where i<j. Our Refined Burgin Machines (RBMs) compute more functions than Turing machines, but fewer than Burgin’s simple inductive Turing machines. We argue that RBMs more closely align with both human and electronic computers than Turing machines do. Consequently, RBMs challenge the dominance of Turing machines in computer science and beyond.

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2

Vitanyi, Paul. "Turing machine." Scholarpedia 4, no. 3 (2009): 6240. http://dx.doi.org/10.4249/scholarpedia.6240.

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3

Kurgaev, A. F., and S. N. Grygoryev. "The universal turing machine interpreter." Reports of the National Academy of Sciences of Ukraine, no. 10 (November 16, 2016): 28–34. http://dx.doi.org/10.15407/dopovidi2016.10.028.

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4

ROBINSON, RAPHAEL M. "MINSKY'S SMALL UNIVERSAL TURING MACHINE." International Journal of Mathematics 02, no. 05 (October 1991): 551–62. http://dx.doi.org/10.1142/s0129167x91000302.

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Marvin L. Minsky constructed a 4-symbol 7-state universal Turing machine in 1962. It was first announced in a postscript to [2] and is also described in [3, Sec. 14.8]. This paper contains everything that is needed for an understanding of his machine, including a complete description of its operation. Minsky's machine remains one of the minimal known universal Turing machines. That is, there is no known such machine which decreases one parameter without increasing the other. However, Rogozhin [6], [7] has constructed seven universal machines with the following parameters: [Formula: see text] His 4-symbol 7-state machine is somewhat different from Minsky's, but all of his machines use a construction similar to that used by Minsky. The following corrections should be noted: First machine, for q 6 00Lq 1 read q 6 00Lq 7; second machine, for q 4 11Rq 4 read q 4 11Rq 10; last machine, for q 2 b 2 bLq 2 read [Formula: see text]. A generalized Turing machine with 4 symbols and 7 states, closely related to Minsky's, was constructed and used in [5].

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5

Beggs, Edwin, José Félix Costa, Bruno Loff, and John V. Tucker. "Computational complexity with experiments as oracles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2098 (June 24, 2008): 2777–801. http://dx.doi.org/10.1098/rspa.2008.0085.

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We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of AD machine are studied, in which physical parameters can be set exactly and approximately. Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines.

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6

Thiagarajan, P. S. "The Turing machine." Resonance 2, no. 7 (July 1997): 3–4. http://dx.doi.org/10.1007/bf02838584.

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7

ITO, AKIRA, KATSUSHI INOUE, ITSUO TAKANAMI, and YUE WANG. "THE EFFECT OF INKDOTS FOR TWO-DIMENSIONAL AUTOMATA." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 05 (October 1995): 777–96. http://dx.doi.org/10.1142/s0218001495000328.

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Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

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8

CALUDE, CRISTIAN S., and LUDWIG STAIGER. "A note on accelerated Turing machines." Mathematical Structures in Computer Science 20, no. 6 (November 8, 2010): 1011–17. http://dx.doi.org/10.1017/s0960129510000344.

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In this paper we prove that any Turing machine that uses only a finite computational space for every input cannot solve an uncomputable problem even when it runs in accelerated mode. We also propose two ways to define the language accepted by an accelerated Turing machine. Accordingly, the classes of languages accepted by accelerated Turing machines are the closure under Boolean operations of the sets Σ1 and Σ2.

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9

Macura, Wiktor K. "n-Skip Turing Machines." Complex Systems 15, no. 3 (September 15, 2005): 237–44. http://dx.doi.org/10.25088/complexsystems.15.3.237.

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A Turing Machine's head is limited to moving one cell in either direction on the tape for a given iteration. We investigate a form of Turing Machine where the head is allowed to move n cells in either direction. We find that such Turing Machines, named n-Skip Turing Machines, are capable of exhibiting complex behavior for simple initial conditions with two states and two colors.

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10

De Brito, Vasco Boavida, José Félix Costa, and Diogo Poças. "The Power of Machines That Control Experiments." International Journal of Foundations of Computer Science 33, no. 02 (February 2022): 91–118. http://dx.doi.org/10.1142/s0129054122500010.

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We consider the experimenter (e.g. the experimental physicist) as a Turing machine — the digital component — and the experiment of measurement — the analog component — as an oracle to the Turing machine. The algorithm running in the machine abstracts the experimental method of measurement (encoding the recursive structure of experimental actions) chosen by the experimenter. In this paper we prove that the central analogue-digital complexity classes [Formula: see text], [Formula: see text] and [Formula: see text] can be characterized in terms of protocols to perform measurements controlled by standard Turing machines.

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11

BRUDA, STEFAN D., and SELIM G. AKL. "ON THE NECESSITY OF FORMAL MODELS FOR REAL-TIME PARALLEL COMPUTATIONS." Parallel Processing Letters 11, no. 02n03 (June 2001): 353–61. http://dx.doi.org/10.1142/s0129626401000646.

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We assume the multitape real-time Turing machine as a formal model for parallel real-time computation. Then, we show that, for any positive integer k, there is at least one language Lk which is accepted by a k-tape real-Turing machine, but cannot be accepted by a (k - 1)-tape real-time Turing machine. It follows therefore that the languages accepted by real-time Turing machines form an infinite hierarchy with respect to the number of tapes used. Although this result was previously obtained elsewhere, our proof is considerably shorter, and explicitly builds the languages Lk. The ability of the real-time Turing machine to model practical real-time and/or parallel computations is open to debate. Nevertheless, our result shows how a complexity theory based on a formal model can draw interesting results that are of more general nature than those derived from examples. Thus, we hope to offer a motivation for looking into realistic parallel real-time models of computation.

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12

Wang, Dong-Sheng. "A local model of quantum Turing machines." Quantum Information and Computation 20, no. 3&4 (March 2020): 213–29. http://dx.doi.org/10.26421/qic20.3-4-3.

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The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.

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Liagkou, Vasiliki, Panayotis E. Nastou, Paul Spirakis, and Yannis C. Stamatiou. "How Hard Is It to Detect Surveillance? A Formal Study of Panopticons and Their Detectability Problem." Cryptography 6, no. 3 (August 20, 2022): 42. http://dx.doi.org/10.3390/cryptography6030042.

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The Panopticon (which means “watcher of everything”) is a well-known prison structure of continuous surveillance and discipline studied by Bentham in 1785. Today, where persistent, massive scale, surveillance is immensely facilitated by new technologies, the term Panopticon vaguely characterizes institutions with a power to acquire and process, undetectably, personal information. In this paper we propose a theoretical framework for studying Panopticons and their detectability status. We show, based on the Theory of Computation, that detecting Panopticons, modelled either as a simple Turing Machine or as an Oracle Turing Machine, is an undecidable problem. Furthermore, we show that for each sufficiently expressive formal system, we can effectively construct a Turing Machine for which it is impossible to prove, within the formal system, its Panopticon status. Finally, we discuss how Panopticons can be physically detected by the heat they dissipate each time they acquire, effortlessly, information in the form of an oracle and we investigate their detectability status with respect to a more powerful computational model than classical Turing Machines, the Infinite Time Turing Machines (ITTMs).

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14

Yashchyk, Oleksandr B. "МАШИНА ТЮРІНГА ЯК УНІВЕРСАЛЬНИЙ ВИКОНАВЕЦЬ АЛГОРИТМІВ ТА ЇЇ ЗАСТОСУВАННЯ В ПРОЦЕСІ ПОГЛИБЛЕНОГО ВИВЧЕННЯ АЛГОРИТМІЗАЦІЇ І ОСНОВ ПРОГРАМУВАННЯ СТАРШОКЛАСНИКАМИ." Information Technologies and Learning Tools 52, no. 2 (May 3, 2016): 10. http://dx.doi.org/10.33407/itlt.v52i2.1365.

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The article discusses the importance of studying the notion of algorithm and its formal specification using Turing machines. In the article it was identified the basic hypothesis of the theory of algorithms for Turing as well as reviewed scientific research of modern scientists devoted to this issue and found the main principles of the Turing machine as an abstract mathematical model. The process of forming information competencies components, information culture and students` logical thinking development with the inclusion of the topic “Study and Application of Turing machine as Universal Algorithm Executor” in the course of Informatics was analyzed.

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15

Aleksander, Igor. "From Turing to Conscious Machines." Philosophies 7, no. 3 (May 29, 2022): 57. http://dx.doi.org/10.3390/philosophies7030057.

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In the period between Turing’s 1950 “Computing Machinery and Intelligence” and the current considerable public exposure to the term “artificial intelligence (AI)”, Turing’s question “Can a machine think?” has become a topic of daily debate in the media, the home, and, indeed, the pub. However, “Can a machine think?” is sliding towards a more controversial issue: “Can a machine be conscious?” Of course, the two issues are linked. It is held here that consciousness is a pre-requisite to thought. In Turing’s imitation game, a conscious human player is replaced by a machine, which, in the first place, is assumed not to be conscious, and which may fool an interlocutor, as consciousness cannot be perceived from an individual’s speech or action. Here, the developing paradigm of machine consciousness is examined and combined with an extant analysis of living consciousness to argue that a conscious machine is feasible, and capable of thinking. The route to this utilizes learning in a “neural state machine”, which brings into play Turing’s view of neural “unorganized” machines. The conclusion is that a machine of the “unorganized” kind could have an artificial form of consciousness that resembles the natural form and that throws some light on its nature.

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16

Welch, Philip. "Characterisations of variant transfinite computational models: Infinite time Turing, ordinal time Turing, and Blum–Shub–Smale machines." Computability 10, no. 2 (April 16, 2021): 159–80. http://dx.doi.org/10.3233/com-200301.

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We consider how changes in transfinite machine architecture can sometimes alter substantially their capabilities. We approach the subject by answering three open problems touching on: firstly differing halting time considerations for machines with multiple as opposed to single heads, secondly space requirements, and lastly limit rules. We: 1) use admissibility theory, Σ 2 -codes and Π 3 -reflection properties in the constructible hierarchy to classify the halting times of ITTMs with multiple independent heads; the same for Ordinal Turing Machines which have On length tapes; 2) determine which admissible lengths of tapes for transfinite time machines with long tapes allow the machine to address each of their cells – a question raised by B. Rin; 3) characterise exactly the strength and behaviour of transfinitely acting Blum–Shub–Smale machines using a Liminf rule on their registers – thereby establishing there is a universal such machine. This is in contradistinction to the machine using a ‘continuity’ rule which fails to be universal.

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17

Mélès, Baptiste. "Les langages de Turing." Intellectica. Revue de l'Association pour la Recherche Cognitive 72, no. 1 (2020): 81–110. http://dx.doi.org/10.3406/intel.2020.1947.

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Si les machines de Turing sont réputées inutilisables, c'est parce qu''on prête souvent davantage attention à la rudimentaire description initiale proposée par leur inventeur qu'à son souci constant d'adapter la syntaxe de leur description aux objectifs poursuivis. Nous décrirons chacun des langages successivement adoptés par Turing en en explicitant la grammaire, en justifiant chaque innovation syntaxique et en confrontant aux déclarations d'intention de Turing sa pratique effective. L'exposition de ces langages sera également éclairée, à titre pédagogique, par la théorie moderne des langages de programmation. Nous verrons ainsi que Turing a proposé trois familles de langages pour décrire le fonctionnement de ses machines : d'abord tout une pyramide de langages explicatifs («tables complètes» et «tables abrégées»), voués à rendre intelligible au lecteur humain le fonctionnement des machines ; puis un langage calculatoire, seul véritable «langage de programmation», permettant notamment l'exécution d''une description de machine par une autre machine ; enfin un langage démonstratif, réservé au mathématicien pour la mise au jour de propriétés des nombres calculables.

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18

Whyman, Richard. "Physical Computational Complexity and First-order Logic." Fundamenta Informaticae 181, no. 2-3 (August 4, 2021): 129–61. http://dx.doi.org/10.3233/fi-2021-2054.

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We present the concept of a theory machine, which is an atemporal computational formalism that is deployable within an arbitrary logical system. Theory machines are intended to capture computation on an arbitrary system, both physical and unphysical, including quantum computers, Blum-Shub-Smale machines, and infinite time Turing machines. We demonstrate that for finite problems, the computational power of any device characterisable by a finite first-order theory machine is equivalent to that of a Turing machine. Whereas for infinite problems, their computational power is equivalent to that of a type-2 machine. We then develop a concept of complexity for theory machines, and prove that the class of problems decidable by a finite first order theory machine with polynomial resources is equal to 𝒩𝒫 ∩ co-𝒩𝒫.

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19

Abdelaziz, Mahmoud, Amr Badr, and Ibrahim Farag. "A Membrane Turing Machine." International Journal of Applied Information Systems 6, no. 4 (October 10, 2013): 1–6. http://dx.doi.org/10.5120/ijais13-451031.

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20

Bhattacharyya, Malay. "Simulating a Turing machine." XRDS: Crossroads, The ACM Magazine for Students 18, no. 3 (March 2012): 43–45. http://dx.doi.org/10.1145/2090276.2090290.

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21

Molina, Abel, and John Watrous. "Revisiting the simulation of quantum Turing machines by quantum circuits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20180767. http://dx.doi.org/10.1098/rspa.2018.0767.

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Yao's 1995 publication ‘Quantum circuit complexity’ in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science , pp. 352–361, proved that quantum Turing machines and quantum circuits are polynomially equivalent computational models: t ≥ n steps of a quantum Turing machine running on an input of length n can be simulated by a uniformly generated family of quantum circuits with size quadratic in t , and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in t , rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of method described by Arright, Nesme and Werner in 2011 in Journal of Computer and System Sciences 77 , 372–378. ( doi:10.1016/j.jcss.2010.05.004 ), that allows for the localization of causal unitary evolutions.

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22

Curtis, Mike. "Turing's Machine." Journal of Humanistic Mathematics 11, no. 1 (January 2021): 440. http://dx.doi.org/10.5642/jhummath.202101.27.

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23

Cabessa, Jérémie, and Hava T. Siegelmann. "The Computational Power of Interactive Recurrent Neural Networks." Neural Computation 24, no. 4 (April 2012): 996–1019. http://dx.doi.org/10.1162/neco_a_00263.

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In classical computation, rational- and real-weighted recurrent neural networks were shown to be respectively equivalent to and strictly more powerful than the standard Turing machine model. Here, we study the computational power of recurrent neural networks in a more biologically oriented computational framework, capturing the aspects of sequential interactivity and persistence of memory. In this context, we prove that so-called interactive rational- and real-weighted neural networks show the same computational powers as interactive Turing machines and interactive Turing machines with advice, respectively. A mathematical characterization of each of these computational powers is also provided. It follows from these results that interactive real-weighted neural networks can perform uncountably many more translations of information than interactive Turing machines, making them capable of super-Turing capabilities.

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24

Nah, JeongEun. "An electrical brain, The beginning of Artificial Intelligence: Based on the movie <The Imitation Game>." Korean Association for Literacy 14, no. 3 (June 30, 2023): 271–87. http://dx.doi.org/10.37736/kjlr.2023.06.14.3.06.271.

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The movie ‘The Imitation Game’ deals with the story of British mathematician and cryptographer Alan Turing. During World War II, he was the protagonist who led the war to victory by deciphering Enigma, an impregnable code system. Computer science with the historical story of Alan Turing, such as the agony of a genius mathematician, curiosity about the problem that there might be a relationship between encryption and decryption, an approach to solving a fundamental problem, and teamwork with colleagues who understand and support it. This is a movie that explains the early status of the computer(calculation machine). In this film, Turing, who created a theoretical model to solve a problem, shows the process of making an effort to realize it. The advent of the modern computer, which is still in use today, is well depicted in this film. Turing thought of a machine that could be applied to everything, not just one. The machine is not programmable, it’s re-programmable. Beyond this, his question that machines cannot think the way humans think, but machines can imitate and think differently is a challenge to us today and was the beginning of today's Computer Science and Artificial Intelligence.

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Warwick, Kevin, and Huma Shah. "The Turing Test." International Journal of Synthetic Emotions 5, no. 1 (January 2014): 31–45. http://dx.doi.org/10.4018/ijse.2014010105.

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This paper appraises some of the prevailing ideas surrounding one of Turing's brilliant ideas, his imitation game experiment, and considers judge performance in assessing machine thinking in the light of practical Turing tests. The emphasis is not on philosophical aspects as to whether machines can think or not but rather on the nature of the discourses performed in the game. Here the authors are more concerned with the nature of human communication and attempts by machines to behave in the same way. In particular the authors look at some of the strategies that Turing suggested would not be good and he has been proved correct. Also authors look at the side track argument, that some have misguidedly introduced, regarding identifying the difference between females and males through such discourse.

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26

Manea, Florin. "On Turing Machines Deciding According to the Shortest Computations." Axioms 10, no. 4 (November 13, 2021): 304. http://dx.doi.org/10.3390/axioms10040304.

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In this paper we propose and analyse from the computational complexity point of view several new variants of nondeterministic Turing machines. In the first such variant, a machine accepts a given input word if and only if one of its shortest possible computations on that word is accepting; on the other hand, the machine rejects the input word when all the shortest computations performed by the machine on that word are rejecting. We are able to show that the class of languages decided in polynomial time by such machines is PNP[log]. When we consider machines that decide a word according to the decision taken by the lexicographically first shortest computation, we obtain a new characterization of PNP. A series of other ways of deciding a language with respect to the shortest computations of a Turing machine are also discussed.

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27

Welch, P. D. "Eventually infinite time Turing machine degrees: infinite time decidable reals." Journal of Symbolic Logic 65, no. 3 (September 2000): 1193–203. http://dx.doi.org/10.2307/2586695.

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AbstractWe characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the Lζ-stables. It also implies that the machines devised are “Σ2 Complete” amongst all such other possible machines. It is shown that least upper bounds of an “eventual jump” hierarchy exist on an initial segment.

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Lechte, John. "Photography from the Turin Shroud to the Turing Machine, Yanai Toister (2020)." Philosophy of Photography 11, no. 1 (June 1, 2020): 137–41. http://dx.doi.org/10.1386/pop_00034_5.

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Tharani, Pooja. "Model of Computation-Turing Machine." IOSR Journal of Computer Engineering 16, no. 1 (2014): 26–30. http://dx.doi.org/10.9790/0661-16122630.

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Suyama, A. "3P350 Autonomous DNA Turing machine." Seibutsu Butsuri 45, supplement (2005): S291. http://dx.doi.org/10.2142/biophys.45.s291_2.

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Hamada, Mohamed. "Turing Machine and Automata Simulators." Procedia Computer Science 18 (2013): 1466–74. http://dx.doi.org/10.1016/j.procs.2013.05.314.

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32

Copeland, B. Jack, and Richard Sylvan. "Beyond the universal Turing machine." Australasian Journal of Philosophy 77, no. 1 (March 1999): 46–66. http://dx.doi.org/10.1080/00048409912348801.

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Figueroa, Ricardo Q., Daniel A. Zamorano, Genaro J. Martínez, and Andrew Adamatzky. "CULET: Cubelet Lego Turing Machine." Proceedings of International Conference on Artificial Life and Robotics 24 (January 10, 2019): 618–21. http://dx.doi.org/10.5954/icarob.2019.gs1-3.

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34

Nirenberg, Robert M. "A practical turing machine representation." ACM SIGACT News 17, no. 3 (January 1986): 35–44. http://dx.doi.org/10.1145/382254.382805.

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35

Qu, Peng, Jin Yan, You-Hui Zhang, and Guang R. Gao. "Parallel Turing Machine, a Proposal." Journal of Computer Science and Technology 32, no. 2 (March 2017): 269–85. http://dx.doi.org/10.1007/s11390-017-1721-3.

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36

SHARMA, AJEET K., and DEBASHISH CHOWDHURY. "TEMPLATE-DIRECTED BIOPOLYMERIZATION: TAPE-COPYING TURING MACHINES." Biophysical Reviews and Letters 07, no. 03n04 (December 2012): 135–75. http://dx.doi.org/10.1142/s1793048012300083.

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DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.

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MARGENSTERN, MAURICE, and LIOUDMILA PAVLOTSKAÏA. "ON THE OPTIMAL NUMBER OF INSTRUCTIONS FOR UNIVERSAL TURING MACHINES CONNECTED WITH A FINITE AUTOMATON." International Journal of Algebra and Computation 13, no. 02 (April 2003): 133–202. http://dx.doi.org/10.1142/s0218196703001262.

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In this paper, a new computation system is defined by coupling a finite automaton with a deterministic Turing machine with one head and one tape that is infinite in one direction only. In a first part of the paper, it is shown that there is a Turing machine with five instructions for which it is possible to devise a finite automaton such that the resulting computation is able to simulate any Turing machine. In a second part of the paper it is shown that if the Turing machine has at most four instructions, whatever the finite automaton is, the halting of the resulting computation is always decidable.

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38

Siomau, Michael. "Undecidable, Unrecognizable, and Quantum Computing." Quantum Reports 2, no. 3 (July 1, 2020): 337–42. http://dx.doi.org/10.3390/quantum2030023.

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Quantum computing allows us to solve some problems much faster than existing classical algorithms. Yet, the quantum computer has been believed to be no more powerful than the most general computing model—the Turing machine. Undecidable problems, such as the halting problem, and unrecognizable inputs, such as the real numbers, are beyond the theoretical limit of the Turing machine. I suggest a model for a quantum computer, which is less general than the Turing machine, but may solve the halting problem for any task programmable on it. Moreover, inputs unrecognizable by the Turing machine can be recognized by the model, thus breaking the theoretical limit for a computational task. A quantum computer is not just a successful design of the Turing machine as it is widely perceived now, but is a different, less general but more powerful model for computing, the practical realization of which may need different strategies than those in use now.

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Iriyama, Satoshi, and Masanori Ohya. "Language Classes Defined by Generalized Quantum Turing Machine." Open Systems & Information Dynamics 15, no. 04 (December 2008): 383–96. http://dx.doi.org/10.1142/s1230161208000262.

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Ohya and Volovich proposed a quantum algorithm with chaotic amplification to solve the SAT problem, which went beyond the notion of the usual quantum algorithm. In this paper, we generalize quantum Turing machines by rewriting the usual quantum Turing automaton in terms of a channel transformation. Moreover, we define some computational classes of generalized quantum Turing machines and show that we can describe the Ohya-Volovich (OV) SAT algorithm with completely positive channels.

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Mikkilineni, Rao. "Going beyond Church–Turing Thesis Boundaries: Digital Genes, Digital Neurons and the Future of AI." Proceedings 47, no. 1 (May 11, 2020): 15. http://dx.doi.org/10.3390/proceedings2020047015.

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The Church–Turing thesis deals with computing functions that are described by a list of formal, mathematical rules or sequences of event-driven actions such as modeling, simulation, business workflows, etc. All algorithms that are Turing computable fall within the boundaries of the Church–Turing thesis. There are two paths to pushing the boundaries. The first is to address the limitation in the clause “ignoring resource limitations”. The second is to search for computing models that solve problems that no ordinary Turing machine can solve using superrecursive algorithms. We argue that “structural machines” provide a new solution to managing both without disrupting the computation itself.

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Mikkilineni, Rao. "Going beyond Church–Turing Thesis Boundaries: Digital Genes, Digital Neurons and the Future of AI." Proceedings 47, no. 1 (May 11, 2020): 15. http://dx.doi.org/10.3390/proceedings47010015.

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The Church–Turing thesis deals with computing functions that are described by a list of formal, mathematical rules or sequences of event-driven actions such as modeling, simulation, business workflows, etc. All algorithms that are Turing computable fall within the boundaries of the Church–Turing thesis. There are two paths to pushing the boundaries. The first is to address the limitation in the clause “ignoring resource limitations”. The second is to search for computing models that solve problems that no ordinary Turing machine can solve using superrecursive algorithms. We argue that “structural machines” provide a new solution to managing both without disrupting the computation itself.

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Miyadera, Takayuki, and Masanori Ohya. "On Halting Process of Quantum Turing Machine." Open Systems & Information Dynamics 12, no. 03 (September 2005): 261–64. http://dx.doi.org/10.1007/s11080-005-0923-2.

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We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, cannot avoid the notion of halting to be probabilistic in Quantum Turing Machine.

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Castro, Paulo. "Lying, computers and self-awareness." Kairos. Journal of Philosophy & Science 24, no. 1 (December 1, 2020): 10–34. http://dx.doi.org/10.2478/kjps-2020-0009.

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Abstract From the initial analysis of John Morris in 1976 about if computers can lie, I have presented my own treatment of the problem using what can be called a computational lying procedure. One that uses two Turing Machines. From there, I have argued that such a procedure cannot be implemented in a Turing Machine alone. A fundamental difficulty arises, concerning the computational representation of the self-knowledge a machine should have about the fact that it is lying. Contrary to Morris’ claim, I have thus suggested that computers – as far as they are Turing Machines – cannot lie. Consequently, I have claimed that moral agency attribution to a robot or any other automated AI system, cannot be made, strictly grounded on imitating behaviors. Self-awareness as an ontological grounding for moral attribution must be evoked. This can pose a recognition problem from our part, should the sentient system be the only agent capable of acknowledging its own sentience.

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Gulcehre, Caglar, Sarath Chandar, Kyunghyun Cho, and Yoshua Bengio. "Dynamic Neural Turing Machine with Continuous and Discrete Addressing Schemes." Neural Computation 30, no. 4 (April 2018): 857–84. http://dx.doi.org/10.1162/neco_a_01060.

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We extend the neural Turing machine (NTM) model into a dynamic neural Turing machine (D-NTM) by introducing trainable address vectors. This addressing scheme maintains for each memory cell two separate vectors, content and address vectors. This allows the D-NTM to learn a wide variety of location-based addressing strategies, including both linear and nonlinear ones. We implement the D-NTM with both continuous and discrete read and write mechanisms. We investigate the mechanisms and effects of learning to read and write into a memory through experiments on Facebook bAbI tasks using both a feedforward and GRU controller. We provide extensive analysis of our model and compare different variations of neural Turing machines on this task. We show that our model outperforms long short-term memory and NTM variants. We provide further experimental results on the sequential [Formula: see text]MNIST, Stanford Natural Language Inference, associative recall, and copy tasks.

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Beggs, Edwin, José Félix Costa, Bruno Loff, and J. V. Tucker. "Computational complexity with experiments as oracles. II. Upper bounds." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2105 (February 25, 2009): 1453–65. http://dx.doi.org/10.1098/rspa.2008.0412.

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Earlier, to explore the idea of combining physical experiments with algorithms, we introduced a new form of analogue–digital (AD) Turing machine. We examined in detail a case study where an experimental procedure, based on Newtonian kinematics, is used as an oracle with classes of Turing machines. The physical cost of oracle calls was counted and three forms of AD queries were studied, in which physical parameters can be set exactly and approximately. Here, in this sequel, we complete the classification of the computational power of these AD Turing machines and determine precisely what they can compute, using non-uniform complexity classes and probabilities.

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Li, Deyi, Jialun Yin, Tianlei Zhang, Wei Han, and Hong Bao. "The Four Most Basic Elements In Machine Cognition." Data Intelligence 6, no. 2 (2024): 297–319. http://dx.doi.org/10.1162/dint_a_00254.

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ABSTRACT The widespread use of ChatGPT has normalized the dialogue Turing test. To meet this challenge, China's major national development strategy suggests that for a new generation of artificial intelligence, it is first necessary to answer the big questions raised by Turing in 1950 from the perspective of cognitive physics: Can machines think? How do machines think? How do machines cognize? Whether it is carbon-based human cognition or silicon-based machine cognition, it is an interaction between complex constructs composed of the four most basic elements: matter, energy, structure, and time. Both humans and machines depend on negative entropy for living, and time is the cornerstone of cognition. Structure and time are parasitic on matter and energy in physical space, forming hard-structured ware. The soft-structured ware in cognitive space is mind, which is parasitic on the hard-structured ware or other existing soft-structured ware, and constitutes a rich hierarchy of multi-scale feelings, concepts, information, and knowledge. Extending “abstraction” from the symbolic school of artificial intelligence, “association” from the connectionist school, and “interaction” from the behaviorist school, the core of cognition is established on the shoulders of such scientific giants such as Schrödinger, Turing and Wiener. Soft and hard-structured ware interact. Cognitive machine can comprise heterogeneous hard-structured ware, such as field programmable gate arrays (FPGAs), data processing units (DPUs), central processing units (CPUs), graphics processing units (GPUs), tensor processing units (TPUs), and memory. It can also be implanted with the “Baby Cognitive Nucleus” which is hard-structured ware genetically inherited and naturally evolved to form the embodied machine. Then the hard-structured ware is parasitized by rich, multi-scale soft-structured ware. By regulating matter and energy through soft-structured ware, machines produce orderly events, form coordinated and orderly thinking activities. The heterogeneous sensors configured by the machine and the speed of thinking will no longer be trapped by the extreme values of biochemical parameters of carbon-based organisms but will be able to perceive through multi-channel cross-modal means, carry out intense thinking, and maintain cognitive continuity with memory. To generate computational and memory intelligence in cognitive space which can bootstrap, self-reuse and self-replicate, imagination and creativity are improved through memory-constrained computing. The new generation of artificial intelligence will leap beyond mechanized mathematics to automation in thinking and self-driven growth of cognition, and the thinking in the cognitive space and the behavior in the physical space verify each other, from the dialogue Turing test to the embodied Turing test. Humans have entered the intelligent era of human-machine co-creation with cognitive machines iteratively inventing, discovering, and creating alongside scientists, engineers, and skilled craftsmen, each wise in its way, improving thinking ability, and amplifying human energy.

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Ambriola, Vincenzo. "Turing Learning Machines." Substantia 8, no. 2 (August 29, 2024): 5–6. http://dx.doi.org/10.36253/substantia-2817.

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Alan Mathison Turing was born in London on June 23rd, 1912. In 1934, he graduated with top marks from King’s College, University of Cambridge, and in 1936, he obtained his Ph.D. from Princeton University, located in New Jersey, USA. In 1940, he worked at Bletchley Park for the Communications Department, using the Colossus machine to decipher Nazi codes. After the war, he moved to the National Physical Laboratory in Teddington, near London. In 1947, he returned to the University of Cambridge, and in 1951, he went to the University of Manchester. Turing is one of the founding fathers of computer science. He achieved theoretical results that profoundly influenced its development, including technology.

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Finnestad, Sonje, and Eric Neufeld. "The Accidental Philosopher and One of the Hardest Problems in the World." Philosophies 7, no. 4 (July 4, 2022): 76. http://dx.doi.org/10.3390/philosophies7040076.

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Given the difficulties of defining “machine” and “think”, Turing proposed to replace the question “Can machines think?” with a proxy: how well can an agent engage in sustained conversation with a human? Though Turing neither described himself as a philosopher nor published much on philosophical matters, his Imitation Game has stood the test of time. Most understood at that time that success would not come easy, but few would have guessed just how difficult engaging in ordinary conversation would turn out to be. Despite the proliferation of language processing tools, we have seen little progress towards doing well at the Imitation Game. Had Turing instead suggested ability at games or even translation as a proxy for intelligence, his paper might have been forgotten. We argue that these and related problems are amenable to mechanical, though sophisticated, formal techniques. Turing appears to have taken care to select sustained, productive conversation and that alone as his proxy. Even simple conversation challenges a machine to engage in the rich practice of human discourse in all its generality and variety.

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Ali Hussain, Eman, and Yahya Mourad Abdul – Abbass. "On Fuzzy differential equation." Journal of Al-Qadisiyah for computer science and mathematics 11, no. 2 (August 21, 2019): 1–9. http://dx.doi.org/10.29304/jqcm.2019.11.2.540.

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In this paper, we introduce a hybrid method to use fuzzy differential equation, and Genetic Turing Machine developed for solving nth order fuzzy differential equation under Seikkala differentiability concept [14]. The Errors between the exact solutions and the approximate solutions were computed by fitness function and the Genetic Turing Machine results are obtained. After comparing the approximate solution obtained by the GTM method with approximate to the exact solution, the approximate results by Genetic Turing Machine demonstrate the efficiency of hybrid methods for solving fuzzy differential equations (FDE).

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Bergstra, Jan, and Kees Middelburg. "Program Algebra for Turing-Machine Programs." Scientific Annals of Computer Science 19, no. 2 (December 30, 2019): 113–39. http://dx.doi.org/10.7561/sacs.2019.2.113.

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