Church-Turing thesis

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	Alonzo Church - Wikipedia, the free encyclopedia
		He and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative "mechanical processes for computation" had equivalent computational abilities.
		Church's lambda calculus influenced the design of the Lisp family of computer languages as well as functional programming languages in general.
		Church remained a professor of mathematics at Princeton until 1967, when he moved to California.
	en.wikipedia.org /wiki/Alonzo_Church

	Church–Turing thesis - Wikipedia, the free encyclopedia
		The success of the Church–Turing thesis prompted supertheses that extend the thesis, including the conjecture that there is a polynomial transformation from the representation of computable functions in one formalization to their representation in another, and the conjecture that every model of computation can be step-by-step simulated by a Turing machine.
		However, the thesis is a definition and not a theorem, and hence cannot be proved true.
		The universe is not a Turing machine (ie, the laws of physics are not Turing-computable), but incomputable physical events are not "harnessable" for the construction of a hypercomputer.
	en.wikipedia.org /wiki/Church-Turing_thesis

	The Church – Turing Thesis
		There also is no way that the Church – Turing Thesis may be proven mathematically to be true because it is virtually impossible to show that all computable problems in existence can be modeled by a Turing Machine.
		The strategies taken have been to show that either there is a computable function that cannot be modeled by a Turing Machine, or to show that the Church – Turing Thesis leads to a contradiction when it is subjected to mathematical proof techniques.
		But, this thesis is very similar to theories that have been proposed in the natural sciences which in essence are also not provable in the sense of mathematics.
	ucsu.colorado.edu /~stephanb/projects/CSCI5444.htm

	Church-Turing Thesis
		Thesis means it isn’t proven - it is believed to be true.
		It says that a Turing machine has equal powerfulness with a standard computing machine.
	www.mathsci.unco.edu /course/CS101/F01/turing/sld003.htm

	Ray Kurzweil Response to Searle Review
		It is remarkable that Searle refers to the Church-Turing Thesis as a "mathematical result." He must be confusing the Church-Turing Thesis (CTT) with Church and Turing theorems.
		CTT is not a mathematical theorem at all, but rather a philosophical conjecture which relates to a proposed relationship between what a human brain can do and what a Turing machine can do.
		This thesis states that all problems that a human being can solve can be reduced to a set of algorithms, supporting the idea that machine intelligence and human intelligence are essentially equivalent).
	www.kurzweiltech.com /Searle/searle_response_10.htm

	BletchleyPark.net
		The Church-Turing thesis, although is not a proof of algorithm, it remains true in the philosophical sense, since it hasn't been disapproved.
		We have the (1) machines paradigm from Turing, the (2) recursive functions from Church and (3) languages that emerged after Church and Turing.
		Alonzo Church's λ-calculus paper and Alan Turing's "Machines" paper in 1936 connected the informal notion of an algorithm or computable function to a precise definition.
	www.bletchleypark.net /computation/church_turing.html

	Michael Nielsen: Interesting problems: The Church-Turing-Deutsch Principle
		Turing’s arguments were a creditable foundation for the Church-Turing thesis, but they do not rule out the possibility of finding somewhere in Nature a process that cannot be simulated on a Turing machine.
		In mathematics, the assertion of the Church-Turing thesis might be compared to any truly fundamental definition, like that of the integers, or the class of continuous functions.
		So Church and Turing mathematically defined a class of functions — called, unsurprisingly, the “computable functions” — that they claimed corresponded to the class of functions that a human mathematician would reasonably be able to compute.
	www.qinfo.org /people/nielsen/blog/archive/000071.html

	CSC 110 Topic 29
		The Church-Turing Thesis: Any reasonable definition of computable is equivalent to computable by Turing Machine.
		One such definition, proposed by mathematician Alonzo Church in 1936 (the same year that Turing invented the TM), is based on recursive functions instead of Turing machines.
		Computing scientists believe this thesis because, so far, every such reasonable definition is provably equivalent to Turing's definition.
	www.augustana.ab.ca /~hackw/csc110/topic/top29.html

	Turing's Thesis
		Turing's thesis has withstood the test of time and many examinations.
		Turing's argument in support of this thesis follows+.
		They are equivalent to a kind of Turing machine with separate read- and write- heads that move in one direction only, with the tape in between.
	www.cs.hmc.edu /claremont/keller/webBook/ch06/sec06.html

	The Church-Turing Thesis: Breaking the Myth Lambda the Ultimate
		It seems to shoot at fish in a barrel (the so-called "strong" Church-Turing thesis, of which there are actually several, including the rather ill-formed proposition which is debunked in the paper), and while the SCTT as described is indeed ill-formed, this is hardly a remarkable or notable result.
		Turing himself fashioned this limitation to exclude the possibility of what he called O-machines (a Turing machine communiticating with a hyper-Turing "oracle"--such an aggregation would certainly be hyper-Turing in power).
		In either case, the fact that the CTT disclaims IO/interactivity (and Turing's so-called "A" machine was formulated explicitly to avoid it, by requiring inputs to be pre-loaded onto the tape before execution) is well-known.
	lambda-the-ultimate.org /node/view/1038

	The Paradigms and Paradoxes of Intelligence, Part 2: The Church-Turing Thesis
		Turing, along with mathematician and philosopher Alonzo Church, advanced, imdependently, an assertion that has become known as the Church-Turing thesis: If a problem that can be presented to a Turing Machine is not solvable by one, then it is also not solvable by human thought.
		Although the existence of Turing's unsolvable problems is a mathematical certainty, the Church-Turing thesis is not a mathematical proposition at all.
		Accepting this thesis means that there are questions for which answers can be shown to exist but which can never be found (and to date, no human has ever solved one of Turing's unsolvable problems, or at least has never proven that he or she has).
	www.kurzweilai.net /articles/art0256.html

	Church-Turing thesis
		Prev by thread: Re: Copeland's ``The Church-Turing Thesis"
		But any attempt to have the thesis claim that procedures beyond algorithmic ones are Turing computable\register machine computable\etc. seems to reflect a confusion that can be cleared up by reflecting on this history of the emergence of the provably equivalent analyses of the intuitive informal notion of an algorithmic procedure in terms of idealized machines.
		We then came to see that other mathematically precise analyses were demonstrably equivalent to Turing's (and Church's), and some employed the notion of a machine, for ex.
	philo.at /phlo/199803/msg00061.html

	Church's Thesis TM
		or the Church-Turing Thesis is the proposal that the informal notion of "a function that can be computed by an algorithm" (or computed "mechanically") can be identified with the the set of functions computable by a Turing Machine.
	www.rci.rutgers.edu /~cfs/472_html/TM/ChurchTh.html

	church
		The Church-Turing thesis can't be proved mathematically because it asserts the equality of two things, only one of which has a precise definition.
		Historically, Church and Turing hit on their respective theses (Church's thesis, Turing's thesis) independently, using different but equivalent formalisms.
		Nevertheless, to those who believe that the old informal notion of computability has some definite meaning, the Church-Turing thesis is not just an arbitrary definition, but an assumption which might be false, and could conceivably be refuted one day, if someone comes up with a way of computing a Turing-uncomputable function.
	www.math.niu.edu /~rusin/known-math/99/church

	Luciano Floridi
		CTT implies that we shall never be able to provide a formalism F that both captures the former notion and is more powerful than a Turing Machine, where "more powerful" means that all TM-computable functions are F-computable but not vice versa.
		Alan Turing's contributions to computer science are so outstanding that two of his seminal papers, "On Computable Numbers with an application to the Entscheidungsproblem" and "Computing Machinery and Intelligence", have provided the foundations for the development of the theory of computability, recursion functions and artificial intelligence.
		CTT remains a "working hypothesis", still falsifiable if it is possible to prove that there is a class of functions that are effectively computable in the sense of {1,2,3,4} but are not TM-computable.
	www.wolfson.ox.ac.uk /~floridi/ctt.htm

	3.txt
		Evidence in support of the Church-Turing thesis: - it has not been disproved yet, - a few other formalizations of algorithm were proposed, but all of them turn out to be equivalent to the notion of Turing machine, - Turing's argument how TM models a human computer is convincing.
		The Church-Turing Thesis: Algorithm = Computable by some TM That is, everything intuitively computable (using the intuitive notion of an algorithm) can be computed by a TM (and vice versa).
		CMPT 308 Lecture 3 (Turing machine, Church-Turing Thesis) Assigned reading from Sipser's textbook: pp.
	www.cs.sfu.ca /~kabanets/cmpt308/lectures/3.txt

	Church-Turing thesis
		In short, Turing suggested that a machine that could behave in a manner indistinguishable from a human could be considered to be "thinking." For many researchers, the goal is simply to pass the Turing Test.
		The Church Awakens "The AIDS pandemic is the greatest humanitarian crisis," Casey said.
		Imagine a "Turing Test" in which the interrogators must be convinced that the participant is a normally sighted individual.
	www.stargeek.com /item/165629.html

	Church-Turing Thesis is Almost Equivalent to Zuse-Fredkin Thesis
		Since the Church-Turing thesis is widely accepted while the Zuse-Fredkin thesis is not, we propose their "near-equivalence" as a strong argument in support of the Zuse-Fredkin thesis.
		The classical Church-Turing thesis is usually considered to be a successful attempt for mathematical formalization of human thinking and the notion of "abstract mathematical theory".
		And since the C-T thesis is widely accepted, while the Z-F thesis is not, in the field of Digital Physics we use both statements: the first for its well-established, almost universal acceptance, and the second, the Z-F thesis, for its close affinity to the first and its special CA formulation.
	digitalphysics.org /Publications/Petrov/Pet02a1/Pet02a1.htm

	The Church-Turing Thesis
		No one has ever built a machine that could do anything that a Turing machine couldn't, or shown an actual example of a problem that a theoretically constructable machine could do that a Turing machine couldn't.
		The reason, basically, > is that Turing machines work only in integers and are finite while neural > nets, as analog devices, depend on real numbers rather than integers.
		People who have a religious attachment to the notion that humans are more powerful than "mere" machines keep on looking, of course.
	www.cryonet.org /cgi-bin/dsp.cgi?msg=4353

	Tony Santolupo
		The Church-Turing thesis is the brainchild of Alan Turing and Alonzo Church.
		Both Turing and Church reached the hypothesis independently and in different forms.
		Hofstadter, in Gödel, Escher, Bach: an eternal golden braid summarizes the Church-Turing thesis in its tamest form as follows: all mathematics problems can be solved only by doing mathematics
	community.middlebury.edu /~schar/Courses/fs023.F02/paper2/tony.htm

	The Church-Turing Thesis
		Another concept closely related to the Church-Turing Thesis is the AI-Thesis.
		This page has information and links about the Church-Turing Thesis.
		Below are given the different versions of the thesis.
	community.middlebury.edu /~wmohar/THESIS.HTM

	Church-Turing Thesis
		Hypothesis: Any computation that can be carried out by mechanical means can be performed by some Turing machine.
		We could conceivably implement the b instruction set on a Turing machine !
	csg.lcs.mit.edu /%7Edevadas/6.004/Lectures/lect13/sld011.htm

	Home Page - Hypercomputation Research Network (http://hypercomputation.net)
		The confusion of Thesis M with the Church-Turing thesis
		Hypercomputation concerns the study of computation beyond that defined by the Turing machine, and is also known as super-Turing, non-standard or non-recursive computation.
		It is a multi-disciplinary research area with relevance across a wide variety of fields, including computer science, philosophy, physics, electronics, biology, and artifical intelligence.
	www.hypercomputation.net

	Principia Cybernetica Mailing-List Archive: Re: Kampis on Church-Turing thesis
		Principia Cybernetica Mailing-List Archive: Re: Kampis on Church-Turing thesis
		Maybe in reply to: DON MIKULECKY: "Kampis on Church-Turing thesis"
	www.cpm.mmu.ac.uk /~bruce/PRNCYB-L/0772.html

	Original Thesis Writing
		If you are a student struggling with your thesis, then you will be able to identify with this scenario.
		I have read literally thousands of theses during my career; and I know what it takes to get a thesis accepted, what a professor looks for in a thesis and how he ensures that the thesis isn’t plagiarized.
		revisions for your thesis in the event of any deviation from your original order specifications.
	www.originalthesiswriting.com

	Church-Turing thesis
		The Church-Turing Thesis in the Stanford Encyclopedia of Philosophy.
		"Church-Turing thesis", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
		Go to the Dictionary of Algorithms and Data Structures home page.
	www.nist.gov /dads/HTML/churchTuringThesis.html

	Church-Turing thesis
		Interpretation: If any finite model of computation/physical device, can solve some decision problem then a Turing machine can solve that problem.
	www.cs.may.ie /~tnaughton/pres/dcs1999/sld012.htm

	ctt.html
		This paper was originally presented at the Turing Colloquium held at the University of Sussex in April, 1990.
		Revised version in P. Millican and A. Clark (editors), Machines and Thought: The Legacy of Alan Turing, Volume 1, Oxford University Press, 1996, pages 137-164.
		AISB Quarterly (Newsletter of the Society for the Study of Artificial Intelligence and Simulation of Behaviour), No. 74, Autumn 1990, pages 9-19.
	www.dcs.ex.ac.uk /~apgalton/abstracts/ctt.html

	Church-Turing Thesis
		X-Message-Number: 9254 Subject: Church-Turing Thesis Date: Sun, 08 Mar 1998 17:03:54 -0500 From: "Perry E. Metzger" < > > From: Thomas Donaldson < > > Subject: Re: CryoNet #9244 - #9245 > Date: Fri, 6 Mar 1998 22:39:55 -0800 (PST) > > Hi Mike!
		The particular features of the counterexample aren't so > important: what it tells us, more than anything else, is that we cannot make > the ASSUMPTION that Turing machines can emulate everything we find in the > world.
		> > The first thing I thought when I read about the nonTuring neural net was > that it was a counterexample to the notion that not all machines must be > Turing machines.
	www.cryonet.org /cgi-bin/dsp.cgi?msg=9254

	Principia Cybernetica Mailing-List Archive: Kampis on Church-Turing thesis
		Next in thread: Bruce Edmonds: "Re: Kampis on Church-Turing thesis"
		Principia Cybernetica Mailing-List Archive: Kampis on Church-Turing thesis
		Reply: Bruce Edmonds: "Re: Kampis on Church-Turing thesis"
	bruce.edmonds.name /PRNCYB-L/0748.html

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