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How much can analog and hybrid systems be proved (super)Turing
 Applied Mathematics and Computation
, 2006
"... 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 superTuring power must have something unreasonable. Our aim is to discuss how much theoretical computer science can ..."
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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 superTuring power must have something unreasonable. Our aim is to discuss how much theoretical computer science can quantify this, by considering several classes of continuous time dynamical systems, and by studying how much they can be proved Turing or superTuring. 1
Hypercomputation, Unconsciousness and Entertainment Technology
"... 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 about a new kind of field are prese ..."
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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 about a new kind of field are presented and discussed. Human unconscious can be interpreted as tapping in these fields for resonating and spreading information. Assuming that culture is based on collective unconscious I propose designing entertainment technology for a new kind of user experience that can influence the individual unconscious and therefore the collective unconscious as well. Our ALICE project can be seen as a first attempt in this direction.
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
Comparative Analysis of Hypercomputational Systems Submitted in partial fulfilment
"... In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosoph ..."
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In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosophers and scientists are suggesting models of hypothetical computing devices which can outperform the Turing machine, performing some calculations the latter is unable to. The ChurchTuring Thesis, which the Turing machine model embodies, has raised discussions on whether it could be possible to solve undecidable problems which Turing’s model is unable to. Models which could solve these problems, have gone further to claim abilities relating to quantum computing, relativity theory, even the modeling of natural biological laws themselves. These so called ‘hypermachines ’ use hypercomputational abilities to make the impossible possible. Various models belonging to different disciplines of physics, mathematics and philosophy, have been suggested for these theories. My (primarily researchoriented) project is based on the study and review of these different hypercomputational models and attempts to compare the different models in terms of computational power. The project focuses on the ability to compare these models of different disciplines on similar grounds and
How to acknowledge hypercomputation?
, 2007
"... We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models. ..."
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We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
Centre for Discrete Mathematics and Theoretical Computer ScienceOutput concepts for accelerated Turing machines
, 2009
"... The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discu ..."
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The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discussion of either the possible actual use by such a machine of an infinite amount of space, or the difficulty (even if only a finite amount of space is used) of defining an outcome for machines acting like Thomson’s lamp. It is the authors ’ impression that insufficient attention has been paid to introducing a clearly defined counterpart for ATMs of the halting/nonhalting dichotomy for classical Turing computation. This paper tackles the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. Nonstandard integers appear quite useful in this regard and we describe several models of computation using filters.
Output concepts for accelerated Turing machines
, 2009
"... The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discu ..."
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The accelerated Turing machine (ATM) is the workhorse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discussion of either the possible actual use by such a machine of an infinite amount of space, or the difficulty (even if only a finite amount of space is used) of defining an outcome for machines acting like Thomson’s lamp. It is the authors’ impression that insufficient attention has been paid to introducing a clearly defined counterpart for ATMs of the halting/nonhalting dichotomy for classical Turing computation. This paper tackles the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. Nonstandard integers appear quite useful in this regard and we describe several models of computation using filters.
Zeno Squeezing of Cellular Automata
 INT. JOURN. OF UNCONVENTIONAL COMPUTING, VOL. 6, PP. 399–416
, 2010
"... ..."
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, 712
"... We discuss the question of how to operationally validate whether or not a “hypercomputer ” performs better than the known discrete computational models. 1 ..."
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We discuss the question of how to operationally validate whether or not a “hypercomputer ” performs better than the known discrete computational models. 1