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Topic: Universal computation

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	Turing machine - Wikipedia, the free encyclopedia
		A more mathematically-oriented definition with a similar "universal" nature was introduced by Alonzo Church, whose work on lambda calculus intertwined with Turing's in a formal theory of computation known as the Church-Turing thesis.
		An abstract version of the universal Turing machine is the universal function, a computable function which can be used to calculate any other computable function.
		For instance, modern computers are actually instances of a more specific form of computing machine, known as the random access machine.
	en.wikipedia.org /wiki/Universal_computation (2393 words)

	Cellular Automata (1983)
		A computer may be regarded as a system in which definite rules are used to transform an initial sequence of, say, 1's and 0's to a final sequence of 1's and 0's.
		A cellular automaton may be proved capable of universal computation by identifying structures that act as the essential components of digital computers, such as wires, NAND gates, memories, and clocks.
		Thus the behavior of a universal computer given particular input may be determined only in a time of the same order as the time required to run that universal computer explicitly.
	www.stephenwolfram.com /publications/articles/general/83-cellular/7/text.html (1876 words)

	Wired 10.12: God Is the Machine
		From this perspective, computation, which juggles and manipulates these primal bits, is a silent reckoning that uses a small amount of energy to rearrange symbols.
		Their conjecture states that any computation executed by one finite-state machine, writing on an infinite tape (known later as a Turing machine), can be done by any other finite-state machine on an infinite tape, no matter what its configuration.
		Your brain and the physics of a cup being filled with water are equivalent, he says: for your mind to compute a thought and the universe to compute water particles falling, both require the same universal process.
	www.wired.com /wired/archive/10.12/holytech_pr.html (3620 words)

	Twenty Problems in the Theory of Cellular Automata (1985)
		But if the cellular automaton is capable of universal computation, then this computation must in general reduce to a direct simulation of the cellular automaton evolution.
		The capability for universal computation can be used to establish the undecidability of questions about the behaviour of a system.
		To establish undecidability in a system not itself capable of universal computation, one must usually find another system that is capable of universal computation, and show that a reduction of its capabilities does not affect undecidability.
	www.stephenwolfram.com /publications/articles/ca/85-twenty/18/text.html (1039 words)

	Five big questions with pretty simple answers
		However, it is important to understand the novelty of a complex universal computation as envisioned in DM, where a number of fundamental quantities are conserved exactly or exactly on average.
		Computational semi-irreducibility forces a kind of intermediate formalism, sandwiched between a CA model at the bottom and classical physics at the top, that can allow for the kinds of calculations we are able to do in QM.
		Throughout this paper the word universal, as in universal computer or universal computation, is used to describe a computer or computation that can exactly emulate the behavior of any other computer that has slightly less memory.
	www.research.ibm.com /journal/rd/481/fredkin.html (10873 words)

	Roger Banks Proof of Universal Computation in Cellular Automata (Site not responding. Last check: 2007-10-08)
		In computer terms, this is called a read/write head, and it would have to be some kind of interface between all of the autonomous cells of Banks' machine design and the one of us that wants to do something useful with it.
		In our world of general purpose computing, all computers have some method of accessing memory locations to either set them (programming, or marking changes of state) or to read them (output, or carrying over one calculation into the next).
		From what we have seen, universal computation by a CA appears to be unnatural in the sense that it requires a great deal of preparation.
	www.bottomlayer.com /bottom/banks/banks_commentary_04.htm (1460 words)

	Sexual Paradox: Chaos
		In the Britannica Dictionary chaos is ‘a condition of utter disorder or confusion as the unformed primal state of the universe’ citing either utter disorder and confusion or an unfathomable abyss as definitive.
		Computational unpredictability follows from the incapacity of any numerical model to approximate the real flow over increasing time, because of such exponentiating divergence.
		A famous example of complexity with universal computation is Conway’s ‘game of life’ in which a given cell survives if two or three neighbours out of the possible eight are alive and is ‘born’ if precisely three are alive.
	www.dhushara.com /paradoxhtm/chaos.htm (5380 words)

	Theory of Computation
		Universal Turing machines have the ability to simulate any other Turing machine when given a description and set of input data for that other Turing machine.
		A common method for proving a device is universal is to show that it is capable of simulating another device already known to be universal.
		For example, if you were to show a system capable of simulating the components necessary and sufficient to build a computer (gates, timers, etc.) then you would have shown that system to be a universal computer.
	www.theory.org /complexity/cdpt/html/node3.html (1966 words)

	Wolfram's Principle of Computational Equivalence: a Reality Check (Site not responding. Last check: 2007-10-08)
		Universal machines are known since the 1930's, and play a very important role in theoretical computer science.
		Partly, their importance is derived from the fact that any modern computer, including the one you use now to read this page, has no more computing abilities than a humble universal machine, in the sense that there is no function your computer can compute that can't also be computed by a universal machine.
		In rule 110, the vast majority of computations that start with random input result in a finite initial part where gliders interact unpredictably, and an infinite final part where gliders do not interact with each other, and their future state in space and time is completely predictable.
	cogsci.indiana.edu /farg/harry/mat/pce/pce.htm (7631 words)

	[No title]
		This is the problem of decoherence and is a stumbling block for quantum computers as the potential power of quantum computers depends on the quantum parallelism brought about by the coherent state [14].
		Such a computer could be built from the quantum equivalent of the Toffoli gate and by adding a few extra operations that can bring about linear superpositions of 0 and 1 states, the universal quantum computer is complete.
		A quantum computer would, for example, allow the "Hubbard Model" (which describes the movement of electrons within a crystal) to be simulated, a task that is beyond the scope of current conventional computers.
	www.doc.ic.ac.uk /~nd/surprise_97/journal/vol4/spb3 (5889 words)

	Cellular Automata FAQ - Properties
		The Universal CA improves a previous intrinsic universal CA of Albert and Culik [3] where intrinsic means that the universal CA serves as an "interpreter" for CA.
		That is, the universal CA given the "code" of a CA A and the input x simulates the behavior of A on input x.
		Garden of Eden theorems seem to have resulted more as a counterbalance to von Neumann's universal constructor; the reversible machines which they imply seem to have been less of an issue than the fact that some specific automata were <> reversible, and the momentary confusion between the implications of the two concepts.
	cafaq.com /properties/index.php (7016 words)

	Universal Rule
		God Is the Machine: "Digital physicists argue that the universe could well be the ultimate computer, and that all existence is, in essence, a function of computation.
		Adding weight to such suppositions are the theories that all things--equations, multimedia works, even emotions--can be reduced to computation; all materials--be they DNA molecules, human brains, or quantum particles, are capable of computation; and all computation is universal--in other words, any computer can carry out the same computations, regardless of its configuration.
		Wolfram was so taken with this view and the universal computation theory that he declared in "A New Kind of Science" that "All processes, whether they are produced by human effort or occur spontaneously in nature, can be viewed as computation." He further expanded this theory to include all outputs of universal computation.
	radio.weblogs.com /0112083/2002/12/28.html (1149 words)

	* Computer - (Computing): Definition
		Computer programs are simply large lists of instructions for the computer to execute, perhaps with tables of data.
		Computer care tips to help you save on those expensive repair costs to your P.C. As we went to turn the power on to our P.C. it started, then, after a few buzzes and whirls, and a puff of dark grey smoke, it ceased to be...
		Computer speaker sets come in two general varieties; 2/2.1 sets(over a wide range of quality), and "surround," "theater," or "gaming" with 4 or more speakers, which tend to be significantly more expensive...
	en.mimi.hu /computing/computer.html (2931 words)

	The Turing Machine and Universal Computation (Site not responding. Last check: 2007-10-08)
		A Turing machine has the capability to simulate any form of computation, consequently all computers that are presently in use are generalized Turing Machines.
		Turing showed that the Turing Machine could simulate any other computing machine and human beings are also like computers, (Before the publication of Turing’s 1936 paper the term computer was generally applied to human begins), thus the Human computer could also be successfully simulated by the Turing Machine.
		A Quantum computer would be able to perform an infinite search in a finite amount of time and hence would solve the halting problem and would show the computability of incomputable functions.
	www.rit.edu /~maa2454/turing1.html (2867 words)

	Quantum computation: a tutorial
		Imagine a computer whose memory is exponentially larger than its apparent physical size; a computer that can manipulate an exponential set of inputs simultaneously; a computer that computes in the twilight zone of Hilbert space.
		A schematic model of a quantum computer is described as well as some of the subtleties in its programming.
		The Shor algorithm [1,2] for efficiently factoring numbers on a quantum computer is presented in two parts: the quantum procedure within the algorithm and the classical algorithm that calls the quantum procedure.
	www-users.cs.york.ac.uk /~schmuel/comp/comp.html (615 words)

	CBofN - Glossary - U
		Universal Approximation Having the ability to approximate any function to an arbitrary degree of accuracy.
		Universal Computation Capable of computing anything that can in principle be computed; being equivalent in computing power to a Turing machine, the lambda calculus, or a Post production system.
		Universal Computer A computer that is capable of universal computation, which means that given a description of any other computer or program and some data, it can perfectly emulate this second computer or program.
	mitpress.mit.edu /books/flaoh/cbnhtml/glossary-U.html (151 words)

	Trevor F Smith: Exterior: Universal computation
		With this title I don't mean ubiquitous computing (though that is where my head is, of late) but the actual computational capabilities of the universe.
		This post is a synopsis of one experiment demonstrating the type of questions posed by universal computation, but there are many others.
		What is the structure that computes interference and coherence?...
	trevor.smith.name /blog/archives/000163.html (193 words)

	Computers, Science, and Extraterrestrials: An Interview with Stephen Wolfram
		The idea of a universal computer is that you can make a universal tool--a general-purpose object--that you can program to do absolutely anything.
		You see, in the mid-1960s computer time was at a premium, so you had to make things as easy as possible for the computer.
		They've long outlived all the computers they were originally developed for, and all the issues they originally had to address.
	www.stephenwolfram.com /about-sw/interviews/96-2001 (4368 words)

	Joho the Blog: [NKS] Wolfram: Computational Equivalence
		E.g., it predicts that a system with simple rules should be capable of computations equivalent in sophistication to any other computer of equal sophistication.
		You might have thought that to do universal computation you need very complex systems with very complex rules (e.g., lots of logic gates), but instead you can do it with Rule 110 which arises from extremely simple rules.
		You can't keep adding complex rules to get more complex computations; once you get past the threshold at which a system is a universal computer, you can't get any further.
	www.hyperorg.com /blogger/mtarchive/001707.html (1031 words)

	Models of Computation
		The Universal Turing Machine was originally described independently but equivalently by Alan Turing and Emil Post (see Davis 1965 or van Heijenoort 1967 for the original papers).
		Unlike the Universal Turing Machine, which may write any of an infinite set of binary strings on its infinitely long tape, finite automata can display only a strictly finite number of distinct states.
		Whereas the Universal Turing Machine can, for intance, enumerate infinitely many natural numbers by virtue of its unlimited tape capacity, any finite automaton for enumerating natural numbers will always be limited by some largest number beyond which it cannot continue.
	www.mulhauser.net /research/tutorials/turing (421 words)

	Cybernetics - A Definition
		Artificial Intelligence (AI) uses computer technology to strive toward the goal of machine intelligence and considers implementation as the most important result; cybernetics uses epistemology (the limits to how we know what we know) to understand the constraints of any medium (technological, biological, or social) and considers powerful descriptions as the most important result.
		The field of AI first flourished in the 1960s as the concept of universal computation [Minsky 1967], the cultural view of the brain as a computer, and the availability of digital computing machines came together to paint a future where computers were at least as smart as humans.
		However the fashion of symbolic computing rose to squelch perceptron research in the 1960s, followed by its resurgence in the late 1980s.
	www.pangaro.com /published/cyber-macmillan.html (1379 words)

	News & Features: DNA-rule-driven fractals probe biochemical self assembly - computationally & in vitro
		Indeed, the importance of universal computation for autonomous fabrication tasks was recognized in von Neumann's seminal work on self-reproducing automata, where he postulated a universal constructor that, by reading an input tape specifying an algorithm for what to build, could carry out the commands necessary to construct an arbitrary object (von Neumann 1966).
		Furthermore, for fabrication purposes, computation by self-assembly could be used to control the direction and extent of growth, thus allowing arbitrary shapes to be created efficiently (Soloveichik and Winfree 2005)—demonstrating that algorithmic self-assembly is not limited to the simulation of cellular automata or Turing machines.
		The main obstacle currently limiting attempts to compute or fabricate using algorithmic self-assembly is the presence of several types of errors.
	www.iscid.org /boards/ubb-get_topic-f-1-t-000215.html (4500 words)

	SSRN-Emergence and Universal Computation by Cassey Lee
		Attempts to formalize the notion of emergence via algorithmic complexity theory runs into the problem that the Kolmogorov complexity function is not computable.
		The reason for this motivates a closer examination of the link between emergence and universal computation.
		Following Wolfram's pioneering work in the classification of cellular automata behavior, the research programs of Langton and Crutchfield, while incomplete, provide important insights to economists seeking to understand the relevance of emergence and universal computation to their discipline.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=551215 (217 words)

	Daniel Gottesman's Papers
		There is also a refinement of the original procedure for universal computation which allows a shorter proof and often less overhead in the computer.
		This paper shows how to derive a threshold result for fault-tolerant computation when only local (nearest or next-to-nearest neighbor) gates are available in one, two, or three dimensions.
		This paper shows how to perform general quantum computations distributed among a number of people, even when some of them are dishonest and are trying to sabotage the computation.
	www.perimeterinstitute.ca /personal/dgottesman/papers.html (3279 words)

	universal computation and the information age (Site not responding. Last check: 2007-10-08)
		Once in the hands of capitalist enterprises and entrepreneurs, universal computers affected: (Phase I) A revolution in social production (in Japan, N. Europe, and later the US from circa1980), bringing the Ford-Taylor mass-production era to a close.
		We end by considering competing sociological theories regarding the potential created for employees and others in the new economy by universal computation when manifested in societal form; the relation between science, technology and society (philosophical monism); theories of technological determinism, etc.
		The class is open to juniors, seniors and interested graduate students, with sophomores by permission of instructor, and requires active participation in discussions of the readings.
	www-personal.umich.edu /~twod/sof/course_flyer_univ_01nov02f.html (388 words)

	Roger Banks Proof of Universal Computation in Cellular Automata
		Since a computation system can be physically built out of wires, transistors, etc[.], it will be sufficient to show that there are configurations (initial assignments of states to the cells) that act like wires, etc., which can be interconnected to form the computation system." Banks at 13.
		Note that the signal travels on one side of the wire, and the direction of travel is determined by the relative orientation of the two "0" white cells to each other.
		The little "foot" at the left-middle-bottom of the configuration is particularly ingenious, because it is necessary to dampen (extinguish) a stray rebounding signal.
	www.bottomlayer.com /bottom/banks/banks_commentary_03.htm (2865 words)

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