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1. Church-Turing Thesis - Wikipedia
http://nostalgia.wikipedia.org/wiki/Church-Turing_thesis
Church-Turing thesis
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2. ChurchÃ¢ÂÂTuring Thesis - Wikipedia, The Free Encyclopedia
Wikipedia article.
http://en.wikipedia.org/wiki/Church-Turing_thesis
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ChurchÃ¢ÂÂTuring thesis
(Redirected from Church-Turing thesis Jump to: navigation search In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376)
The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by Alonzo Church Stephen Kleene and J.B. Rosser

3. Church-Turing Thesis - Simple English Wikipedia, The Free Encyclopedia
http://simple.wikipedia.org/wiki/Church-Turing_thesis
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From Simple English Wikipedia - the free encyclopedia that anyone can change
Jump to: navigation search The Church-Turing thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a statement about computers . It states that every computer program (every algorithm ) can be remade to run on a simple type of computer known as a Turing machine This short article can be made longer. You can help Wikipedia by adding to it Retrieved from " http://simple.wikipedia.org/wiki/Church-Turing_thesis Category Computer science Views Personal tools Getting around Search Toolbox In other languages

4. Tiny Wikipedia Dump Test
Church s_conjecture ChurchRosser_theorem Church-Turing_Thesis Church-Turing_Thesis Church_Creek,_Maryland Church_Crookham Church_Father Church_Fathers
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6. Spark's Pensieve - Model Of Computation : Ruby
Ever heard of the ChurchTuring Thesis? http//en.wikipedia.org/wiki/Church-Turing_Thesis Turing Machines? http//en.wikipedia.org/wiki/Turing_machine
http://www.thinkingms.com/pensieve/CommentView,guid,563f6495-6cb6-4af8-9a2c-1230
 Spark's Pensieve then take me disappearin' through the smoke rings of my mind... hide menu Saturday, 19 June 2004 Model of Computation : Ruby . You can find it here: http://web.archive.org/web/20030618203059/visibleworkings.com/little-ruby/ (Someday it will be available here: http://www.visibleworkings.com/little-ruby/ Instead of writing the whole thing myself or copy paste it, I ask you to simply go read the book. That is my blog entry for the day. Reading Let me quote from one of the conversation toward the end of the third chapter (the last chapter that is written so far): will always be missing that one feature you simple rules for you to combine lets you "This is the Unix philosophy. Write programs that do one thing and do it well. Write programs to work together. Write programs to handle text streams, because that is a universal interface." Doug McIlroy Prof Daniel P Friedman of Indiana University and Prof Matthias Felleisen of Rice University I did not know this then, but sometime last year I was in email correspondence with Prof Friedman. That time, had I known that he is author of a respected LISP text book, I might have been frightened off the prospect of asking this - Roshan

 7. Read About Computers, Computer Science, Theoretical From Thumbshots.net Preview by Thumbshots.org ChurchTuring Thesis Wikipedia article. http//en.wikipedia.org/wiki/Church-Turing_Thesishttp://www.thumbshots.net/webguide.aspx?cat=Computers/Computer_Science/Theoretic

8. Halfling Rogue
http://www.ljfind.com/user/halfling-rogue/
Main / Search News FAQ Search Form addthis_url = location.href; addthis_title = document.title; addthis_pub = 'leonstar1'; Recent Searches coi phim nguoi lon free ramalan jodoh tajul muluk sarah azhari telanjang gambar rahma azhari telanjang ... otomen Recent topics discussed amazing things arbeit macht frei adore candles
... Advanced search Results 1 - 10 of about 536 (0.0 sec) http://halfling-rogue.livejournal.com/198544.html exams Math final wasn't as bad as I thought. A lot of work, certainly (I had to use all three hours), and probability and standard distribution kicked my ass just like I thought it would, but could have been a lot worse. (Leah was really tricky, giving us a Venn Diagram that was equal to a null set. DX I spent five minutes staring at my answer thinking, 'That CAN'T be right!')
Got 85.5/106 on my 112 final, which More... Published by : halfling-rogue
http://halfling-rogue.livejournal.com/198337.html exams
PWN'D.

 9. A New Kind Of Science: The NKS Forum - The Complexity Of A Living Cell Cannot Be http//en.wikipedia.org/wiki/ChurchTuring_Thesis Although TuringÂs algorithm seems better than that of the Book of Creation, God did use neither algorithm.http://forum.wolframscience.com/printthread.php?s=e290c62cd57e8a26fe7800b97bc287

10. 000000 - Log Started Squeak/06.12.18 001758 - Quit
144339 sittiri http//en.wikipedia.org/wiki/ChurchTuring_Thesis ) 144401 jecel beam-weapon spammming newsgroups is not a good way to get a
http://tunes.org/~nef/logs/squeak/06.12.18
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 11. Question About The Halting Problem - GameDev.Net Discussion Forums http//en.wikipedia.org/wiki/ChurchTuring_Thesis The thesis can be stated as Every function which would naturally be regarded as computable can behttp://www.gamedev.net/community/forums/ViewReply.asp?id=2972259

12. Windows Applications [Archive] - Forums
In a technical sense, the ChurchTuring thesis (http//www.reference. com/browse/wiki/Church-Turing_Thesis) implies that any operating environment can be
http://forum.freespire.org/archive/index.php/t-329.html
 Forums Assistance Freespire OS Issues Other ... PDA View Full Version : Windows applications Guru 12-July-2006, 09:25 Is it possible to run applications developed for windows 98 / nt / xp? If not is this something which is scheduled for future? Im very new to freespire, but quite excited. Im fed up with MS policies. I feel the success of freespire depends a lot on these factors. how easy it is to install messengers like yahoo etc.. and make full use of the application capabilities. I tried the linspire, but was unable to install yahoo or any other messenger. I had to use the inbuilt messenger in linspire. Zug 12-July-2006, 10:45 If I may add an additional query: As a newbie to Linux distros, I've read that Crossover Office MAY yet be a killer app. That is, for users who don't want to leave their MS apron strings! Question: Is Crossover acceptable to Freespire? Dr.Jones 12-July-2006, 14:01 The products in the Freespire repository will work with the OS (including Crossover Office). Bro.Tiag 12-July-2006, 17:03 No one can not run Windows apps nativly in linux. One must do so through some sort of linux application, like Wine, Win4Lin, Crossover, VMware etc. Just so you know. Oh, also some/most of these linux apps cost money to install.

13. Art + Communication : WAVES
7 Wikipedia about Church Turing Thesis http//en.wikipedia. org/wiki/ChurchTuring_Thesis 8 I am sharing this current position to some degree having not
http://rixc.lv/06/en/txt02.html
 WAVES - an introduction The Genesis of the Idea The Art and Science of WAVES Based on this premise, making the WAVES exhibition and event happen is research into one half of what I consider the fundamentals or basics of contemporary practice in art and technology. Waves are literally the medium of media art, on the deepest material level as well as conceptually. Electromagnetic waves occur naturally, they exist, they are everywhere, constantly passing through our bodies, yet with our natural senses we can only perceive heat and light. "what is thought of as "light" is actually a propagating oscillatory disturbance in the electromagnetic field, i.e., an electromagnetic wave. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies." Wikipedia It can surely be no coincidence that this iconoclastic artistic "statement" entered the debate about the nature of the world just as the revolutions in linguistics, physics, psychology and commerce were exploding the rationalist certainties of the 19th century. Robert Adrian 1996 This new situation has been preceded by Gaston Bachelards writing on the Formation of the Scientific Spirit (1934) where he reflected on the consequences of the paradigm change initiated by Einstein, Heisenberg and Bohr. The new scientific worldview is capable of incredible and horrific things, such as taming the atom or unleashing the atomic force in the shape of nuclear explosions. Yet in explaining wave/particle dualism science has still nothing much better to offer than the Copenhagen Interpretation.

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222 Cf. http//en.wikipedia.org/wiki/ChurchTuring_Thesis . As the dual name indicates, two researches had independently come up with solutions;
http://ijlit.oxfordjournals.org/cgi/content/full/14/3/257

16. Is Mathematics Discovered Or Invented? Text - Physics Forums Library
recursive sets and what computers can do. This assumption is essentially the ChurchTuring thesis (http//en.wikipedia.org/wiki/Church-Turing_Thesis).
http://www.physicsforums.com/archive/index.php/t-102552.html
 Physics Help and Math Help - Physics Forums PF Lounge General Discussion Philosophy ... PDA View Full Version : Is Mathematics Discovered or invented? ComputerGeek It is classic, but I would like to know what you all think. invented. but its not as invented as chemistry - damn thats made up! (yes i am a student) selfAdjoint It is classic, but I would like to know what you all think. I b3elieve it's invented, but it FEELS like discovery. And I believe this is so (I have posted this before) because mathematical ideas are by definition WELL-DEFINED. That is they each have a limited and explicit definition agreed on by all, which gives them a sharp-edged character, just like our sensations of a rock or a chair in our environment. So the mind treats them that way and they feel like discoveries. Pengwuino I feel it is a discovery because any invention can be modified to do anything. We don't invent F=ma for example, we discover it... or else we would be perfectly capable of saying F=2ma. Who would be to say we're wrong if its just an invention? Inventions are never "wrong", some are just better then others. Rade I agree with Ayn Rand on this point..."a vast part of higher mathematics...is devoted to the task of discovering methods by which various shapes can be measured" (e.g., integral calculus used to measure area of circles as one example). In this way, the mental process of "concept formation" and "applied mathematics" have a similar goalidentfying relationships to perceptual data.

17. Church-turing Thesis - Interaction-Design.org: A Site About HCI, Usability, UI D
http://www.interaction-design.org/dictionary/church-turing_thesis.html
About Contact Site map References ... Dictionary Church-turing Thesis
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 18. Upto11.net - Wikipedia Article For Article about ChurchTuring_Thesis is Unavailable. We could not find this article in our database. If you feel that you ve reached this page in errorhttp://www.upto11.net/generic_wiki.php?q=church-turing_thesis

19. ChurchÂTuring Thesis
http://www.algebra.com/~pavlovd/wiki/Church-Turing_thesis

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21. Del.icio.us/url/4f1651190c458d9ce3e1dd96722d08cb
ChurchÂTuring thesis Wikipedia, the free encyclopedia. http//en.wikipedia.org/wiki/Church-Turing_Thesis. this url has been saved by 20 people.
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ChurchÃ¢ÂÂTuring thesis - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Church-Turing_thesis
user notes
• on computability and Turing completeness caelumfeles Claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available. andreas.s

22. Comp.lang.lisp: Re: ILC2003: Church Vs Turing Smackdown
http//en2.wikipedia.org/wiki/ChurchTuring_Thesis . In his 1936 paper On Computable Numbers, with an Application to the
http://coding.derkeiler.com/Archive/Lisp/comp.lang.lisp/2003-10/1728.html
Re: ILC2003: Church vs Turing Smackdown
From: Anton van Straaten ( anton_at_appsolutions.com
Date: Date: Fri, 17 Oct 2003 03:25:29 GMT Kenny Tilton wrote:
something.
I don't remember the assertion which prompted the response - I think it was
something that Jay Sulzberger said - but I believe that the gist of
McCarthy's reply was that Church wasn't sure that the lambda calculus was a
complete model for computability, until Turing proposed Turing Machines as a
model for computability, and Turing proved the two equivalent.
There's a summary of the relevant history at
http://en2.wikipedia.org/wiki/Church-Turing_thesis

"In his 1936 paper On Computable Numbers, with an Application to the Entscheidungsproblem Alan Turing tried to capture this notion formally with the introduction of Turing machines. In that paper he showed that the

 23. Alexa - Sites In: Theoretical en.wikipedia.org/wiki/ChurchTuring_Thesis Site info for wikipedia.org Site Info icon. Thumbnail image of bu.edu Theory of Computationhttp://www.alexa.com/browse/general/?&CategoryID=259003&mode=general&R=False&Sta

 24. True Vine Online Directory url en.wikipedia.org/wiki/ChurchTuring_Thesis. Computability Logic. Main web source on the subject overview, downloadable articles, links.http://www.truevine.net/odp/odp/index.cgi?/Computers/Computer_Science/Theoretica

25. Theoretical Web Directory.
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28. ILC2003: Church Vs Turing Smackdown - Interactive Code
http//en2.wikipedia.org/wiki/ChurchTuring_Thesis In his 1936 paper On Computable Numbers, with an Application to the
 Web InteractiveCode.com Interactive Code Programming/Coding Google's Summer of Code ILC2003: Church vs Turing Smackdown ILC2003: Church vs Turing Smackdown Posted by Kenny Tilton on October 16th, 2003 Another thing that sailed over my head but low enough to get my interest was an exchange in which (I am going to mangle this beyond belief) McCarthy corrected something by saying it was not until Turing did something that Church (or somebody) was sure of the lambda calculus. This reminds me of those horrible moments when I try to sing a little bit of a song in a record store to an employee when I can't find something. What was that? It happened so fast I grokked neither the assertion nor the rebuttal. kenny http://tilton-technology.com What?! You are a newbie and you haven't answered my: http://alu.cliki.net/The%20Road%20to%20Lisp%20Survey Posted by Anton van Straaten on October 17th, 2003 Kenny Tilton wrote: I don't remember the assertion which prompted the response - I think it was something that Jay Sulzberger said - but I believe that the gist of McCarthy's reply was that Church wasn't sure that the lambda calculus was a complete model for computability, until Turing proposed Turing Machines as a

 29. Free Keywords ODP : Computers : Computer Science : Theoretical http//en.wikipedia.org/wiki/ChurchTuring_Thesis. Computability Logic Main web source on the subject overview, downloadable articles, links.http://free-keywords.com/dmoz/index.php?c=Computers/Computer_Science/Theoretical

30. Odd Computing Question [Archive] - Bad Astronomy And Universe Today Forum
That sounds like the ChurchTuring thesis (http//en.wikipedia. org/wiki/Church-Turing_Thesis).
http://64.207.216.12/archive/index.php/t-60161.html
 Bad Astronomy and Universe Today Forum Space and Astronomy General Science PDA View Full Version : Odd computing question ASEI 09-June-2007, 03:51 PM I've read statements before about non-Turing-machines being able to solve problems that Turing machines (pretty much encompassing all computers we know of) cannot. But I'm having a hard time understanding what is meant by a non-turing machine: Wouldn't it be possible to simulate any sort of computer on a computer using some sort of state-variable simulation? (Doesn't matter if it's arbitrarily complex). It always seemed to me that computers were general in this way. 09-June-2007, 05:44 PM Wouldn't it be possible to simulate any sort of computer on a computer using some sort of state-variable simulation? That sounds like the Church-Turing thesis (http://en.wikipedia.org/wiki/Church-Turing_thesis). Wikipedia Hypercomputation (http://en.wikipedia.org/wiki/Hypercomputation) is a decent survey of methods to perform non-Turing-computable functions. 09-June-2007, 06:12 PM Wikipedia Hypercomputation (http://en.wikipedia.org/wiki/Hypercomputation) is a decent survey of methods to perform non-Turing-computable functions.From that link:A model more powerful than Turing machines was introduced by Alan Turing in his 1939 paper Systems of logic based on ordinals. This paper investigated mathematical systems in which an oracle was available, which could compute a single arbitrary (non-recursive) function from naturals to naturals. He used this device to prove that even in those more powerful systems, undecidability is present. Turing's writing made it clear that oracle machines were only mathematical abstractions, and were not thought of as physically realisable.

 31. World Culinary Institute url en.wikipedia.org/wiki/ChurchTuring_Thesis. Computability Logic Preview Main web source on the subject overview, downloadable articles, links.http://www.worldculinaryinstitute.com/cgi-bin/odp/index.cgi?base=/Computers/Comp

32. Topsites2007.com On 2007 : Computer Science : Theoretical
http//en.wikipedia.org/wiki/ChurchTuring_Thesis. Computability Theory - Wikipedia article. http//en.wikipedia.org/wiki/Computability_theory
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pages found in Theoretical Computability Theory - Wikipedia article.
http://en.wikipedia.org/wiki/Computability_theory Church-Turing Thesis - Wikipedia article.
http://www.cis.upenn.edu/~giorgi/cl.html Theory of Computation - Lecture notes for an undergraduate class taught by Leonid Levin at UC Berkeley.
http://www.cs.bu.edu/fac/lnd/toc/ Interactive Computation - Wikipedia article.
http://en.wikipedia.org/wiki/Interactive_computation
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•  33. Tylko Najlepsze Strony! : Computers : Computer Science : Theoretical ChurchTuring Thesis http//en.wikipedia.org/wiki/Church-Turing_Thesis. Main web source on the subject overview, downloadable articles, links.http://www.rainfox.eu.org/index.php?c=Computers/Computer_Science/Theoretical

34. Science: Realistic Benefits Of Quantum Computing, By The End Of Year 2008
http//en.wikipedia.org/wiki/ChurchTuring_Thesis. In fact, even the Strong Church-Turing thesis has not been disproven by QC! The only problems that are
 register submit help blog ... stats search remember me recover password login sort by hot new top old other communities Realistic Benefits of Quantum Computing, by the end of year 2008 (techdo.com) 1 point posted 3 months ago by 6 comments info comments related details [deleted] (0 children) [+] [deleted] 3 points 3 months ago The article seems way over-hyped for my tastes, but interesting stuff nonetheless permalink tomashark (5 children) [+] tomashark 1 point 3 months ago Flaming BS. permalink (4 children) [+] 1 point 3 months ago Sorry? permalink parent tomashark (3 children) [+] ... tomashark 1 point 3 months ago The article makes numerous blatantly false claims. It generally misleads the audience into thinking that quantum computing is much more powerful than current science understands it to be. It's a joke: Unlike bits, qubits can represent more than one number at a time, One isolated qubit can store no more than one classical bit of information. That its state can take on a continuum of values is, for storing bits, no more different than saying a weighted coin can take on a continuum of head/tail probabilities p in [0,1]. Quantum computing is very subtle - a lot of things which look quantum are actually also found in classical probabilistic computers.

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37. Sci.logic: Re: Can You Find Anything Wrong With This Solution To The Halting Pro
http//en.wikipedia.org/wiki/ChurchTuring_Thesis Church s Thesis is NOT some prediction that Peter Olcott will eventually fail in his bid to design some
http://sci.tech-archive.net/Archive/sci.logic/2004-07/1970.html
Re: Can you find anything wrong with this solution to the Halting Problem?
From: George Greene ( greeneg_at_greeneg-cs.cs.unc.edu
Date: Date: 18 Jul 2004 17:15:27 -0400
"Peter Olcott" <olcott@worldnet.att.net> writes:
: That is simply not true.
It IS SO TOO true, DUMBASS.
: The conclusion of the original problem
HOW THE ***** would *YOU* know *THAT*
You DON'T KONW *** about the original problem!
You have NEVER SEEN a treatment of "The Original Problem"
that you could get within SNIFFING distance of UNDERSTANDING!
: was that it is completely impossible to always be able to correctly : determine For WHAT to always correctly determine?!?!?! Suppose we had a supernatural oracle that undersood every fact about all Turing Machines: could IT always correctly determine : whether or not any other Turing Machine would halt

 38. Halting Problem Totally Unsolvable? [Logic] http//en.wikipedia.org/wiki/ChurchTuring_Thesis http//en.wikipedia. org/wiki/Hypercomputation I disagree with the other posters that say CPU shttp://www.adras.com/Halting-problem-totally-unsolvable.t2962-94-1.html

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40. Wiki ChurchÂTuring Thesis
Wiki ChurchÂTuring thesis. Contents 1. Formal statement 2. History 2. 1. 19301970 2. 2. Later developments Axiomatizing the notion of effective
http://wapedia.mobi/en/Church-Turing_thesis
 Wiki: ChurchÃ¢ÂÂTuring thesis Contents: 1. Formal statement 2. History 2. 2. Later developments: Axiomatizing the notion of "effective calculation/computation" 3. Success of the thesis ... Wapedia: For Wikipedia on mobile phones

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43. Turing Machine - CompWisdom
his Turing machines in fact describe the same set of functions (Turing 1936, 263ff). http//en2.wikipedia.org/wiki/ChurchTuring_Thesis (1487 words)
http://www.compwisdom.com/topics/Turing-machine
Meaningful results bit by bit AboutÃÂ us WhyÃÂ useÃÂ us? Press ContactÃÂ us
Topic: Turing machine
Universal Turing Machine in XSLT The Turing machine moves its tape head one symbol to the left or to the right, or does not move the tape head, depending on the value of the 'movement' attribute that is returned by the transition function. The source document, which specifies a Turing machine , is an XML document that conforms to the Turing Machine Markup Language (TMML). The input tape for the Turing machine is "199". http://www.unidex.com/turing/utm.htm (914 words)
Tools for Thought by Howard Rheingold: Chapter One
Turing proved that his hypothetical machine is an automated version of a formal system specified by the starting position (the pattern of Os and Xs on the tape at the beginning of the computation ) and the rules (the instructions given by the instruction tables). Turing 's theoretical machine was both an example of his theory of computation and a proof that a certain kind of computing machine could, in fact, be constructed.

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In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as the Church's thesis, Church's conjecture and Turing's thesis) is a hypothesis about the nature of computers , such as a digital computer or a human with a pencil and paper following a set of rules. The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available. The thesis cannot be mathematically proven; it is sometimes proposed as a physical law or as a definition.
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Church-Turing thesis
In computability theory the Church-Turing thesis Church's thesis Church's conjecture or Turing's thesis , named after Alonzo Church and Alan Turing , is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. The thesis claims that any calculation which is possible, can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available. It is generally assumed that an algorithm must satisfy the following requirements:
• The algorithm consists of a finite set of simple and precise instructions that are described with a finite number of symbols. The algorithm will always produce the result in a finite number of steps.
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In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376)
The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by Alonzo Church Stephen Kleene and J.B. Rosser and by Alan Turing . Although Stephen Kleene proved the two theses equivalent, the fundamental

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 The W2N.net Wikipedia Church-Turing thesis edit (Powered By The Rozaleenda Group, Inc. In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376) The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by Alonzo Church Stephen Kleene and J.B. Rosser and by Alan Turing . Although Stephen Kleene proved the two theses equivalent, the fundamental premise behind the theses the notion of "effectively computable" or "effectively calculable" is "a vague intuitive one" based as it is on (i) Ã¢ÂÂheuristic [observational, experiential] evidenceÃ¢ÂÂ, (ii) the Ã¢ÂÂequivalence of Ã¢ÂÂdiverse formulationsÃ¢ÂÂ (e.g. the three computational processes)

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It s neither trivial nor apparently provable (for or against) the ChurchTuring Thesis (http//en.wikipedia.org/wiki/Church-Turing_Thesis) proposes .
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 IIDB IIDB Philosophical Forums Philosophy PDA View Full Version : Essay on CRA, advice appreciated. Jneale February 2, 2005, 05:48 PM John Searle and the Chinese Room: A Defence of Turing and Behaviourism We are entering or indeed are already upon one of the most exciting periods of epistemic history. Epistemology concerns issues that were always considered to be suited to the realm of philosophy, essentially that the concepts it discussed were too abstract in their nature to be considered science. Today these issues are no longer involved in purely philosophical debate but in cognitive science and its derivatives also. I shall refer to the mind as if I was advocating substance dualism, normally associated as part of Descartes meditations; however I donÃ¢ÂÂt wish to enter into a debate over monism, dualism, as it really has no effect on the issues I want to deal with. Every psychological attribute has now, due to considerable recent advances in neuro-anatomical science, been associated with a specific location in the brain. The ability to assimilate visual input with the occipital lobe, the process of sorting objects into categories with the temporal lobe, Intentionality with the parietal lobe and reasoning with the frontal lobe. Even semantics have been associated with activity in parts of the brain. Semantics is a frequently used term in cognitive science and it is important for me to clarify what I intend by the term. Language has two levels, syntax and semantics. Syntax is the sound, series of letters the symbol I use to represent the semantics behind language. When I read this essay you hear the symbols, syntax, and interpret its semantic meaning, when you ask questions at the end you will do so through syntax and I shall be interpreting with semantics. Despite this relationship being made slightly more complex by the presence of an internal monologue the concept remains the same.

59. Church-turing Thesis
The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage
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The Thesis claims that any calculation that is possible can be performed by an Algorithm running on a computer, provided that sufficient time and storage space are available.
It is generally assumed that an algorithm must satisfy the following requirements:
#The algorithm consists of a finite set of simple and precise instructions that are described with a finite number of symbols.
#The algorithm will always produce the result in a finite number of steps.
#The algorithm can in principle be carried out by a human being with only paper and pencil.
#The execution of the algorithm requires no intelligence of the human being except that which is needed to understand and execute the instructions.
The Euclidean Algorithm for determining the Greatest Common Divisor of two Natural Number s is an example of such an algorithm.
This description of algorithm is intuitively clear but lacks formal rigor, since it is not exactly clear what a "simple and precise instruction" is, and what exactly the "required intelligence to execute these instructions" is. (See, for example, Effective Results In Number Theory for cases well beyond the Euclidean algorithm.)

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61. Re: JSH Center For Advanced Research. Looking For An Example Of :
thesis ``Every effectively computable function can be computed by a Turing machine. http//en.wikipedia.org/wiki/ChurchTuring_Thesis David Bernier
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Re: JSH Center for Advanced Research. Looking for an example of :
from [ David Bernier Subject Re: JSH Center for Advanced Research. Looking for an example of : From Date Thu, 14 Sep 2006 06:55:35 -0400 Newsgroups sci.math sci.physics Tim Peters wrote: ... [Proginoskes] [Eric Gisse] Why is the number of algorithms countable as opposed to uncountable? Yes, I know the difference between 'countable' and 'uncountable'. It's for the same reason that the set of all possible books in any given human language is countable: the set of all finite strings composed of symbols from a finite alphabet is countable. An algorithm has to be /specified/ somehow, right? Whether you pick English or a formalism like Turing machines, all possible finite strings from the alphabet you pick are countable. If you allow algorithm specifications of infinite length, you can worm around that but then few would agree that you're still talking about what /they/ mean by "algorithms".

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ChurchÃ¢ÂÂTuring thesis
(Redirected from Church-Turing thesis Jump to: navigation search In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376)
The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by Alonzo Church Stephen Kleene and J.B. Rosser

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ChurchÃ¢ÂÂTuring thesis
(Redirected from Church-Turing thesis Jump to: navigation search In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376)
The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by

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Church-Turing thesis
In computability theory the ChurchÃ¢ÂÂTuring thesis Church's thesis Church's conjecture or Turing's thesis , named after Alonzo Church and Alan Turing , is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available. It is generally assumed that an algorithm must satisfy the following requirements:
• The algorithm consists of a finite set of simple and precise instructions that are described with a finite number of symbols. The algorithm will always produce the result in a finite number of steps. The algorithm can in principle be carried out by a human being with only paper and pencil. The execution of the algorithm requires no intelligence of the human being except that which is needed to understand and execute the instructions.
• An example of such a method is the Euclidean algorithm for determining the greatest common divisor of two natural numbers This description of algorithm is intuitively clear but lacks formal rigor, since it is not exactly clear what a "simple and precise instruction" is, and what exactly the "required intelligence to execute these instructions" is. (See for example

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In computability theory the 'ChurchÃ¢ÂÂTuring thesis' (also known as 'Church's thesis', 'Church's conjecture' and 'Turing's thesis') is a combined

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ChurchÃ¢ÂÂTuring thesis
(Redirected from Church-Turing thesis Jump to: navigation search In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

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ChurchÃ¢ÂÂTuring thesis
(Redirected from Church-Turing thesis Jump to: navigation search In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. " (Kleene 1952:376)
The three computational processes (recursion, ÃÂ»-calculus, and Turing machine) were shown to be equivalent by Alonzo Church Stephen Kleene and J.B. Rosser

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81. Church-Turing Thesis - Gurupedia
The ChurchTuring thesis is an idea in computer science named after the mathematicians Alonzo Church and Alan Turing. In its most common form,
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Church-Turing thesis
The Church-Turing thesis is an idea in computer science named after the mathematicians Alonzo Church and Alan Turing . In its most common form, it states that every effective computation or algorithm can be carried out by a Turing machine . Any computer program in any of the conventional programming languages can be translated into a Turing machine, and any Turing machine can be translated into most programming languages, so the thesis is equivalent to saying that the conventional programming languages are sufficient to express any algorithm. The thesis, which is now generally assumed to be true, is also known as Church's thesis or Church's conjecture and Turing's thesis Table of contents 1 Equivalent forms of the thesis 2 Origins of the thesis 3 Success of the thesis 4 Philosophical implications ... 7 See also
Equivalent forms of the thesis
The thesis might be rephrased as saying that the notion of effective or mechanical method in logic and mathematics is captured by Turing machines. It is generally assumed that such methods must satisfy the following requirements:
• The method consists of a finite set of simple and precise instructions that are described with a finite number of symbols.
•  82. Turing Machine Simulation Used In A Breadth First Computer Science Course ChurchTuring Thesis, http//en.wikipedia.org/wiki/ChurchTuring_thesis, June 2006. A description of the Church-Turing Thesis.http://portal.acm.org/citation.cfm?id=1181845

83. ChurchÃ¢ÂÂTuring Thesis
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ChurchÃ¢ÂÂTuring thesis
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In computability theory the ChurchÃ¢ÂÂTuring thesis (also known as Church's thesis Church's conjecture and Turing's thesis ) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's ÃÂ»-calculus
Church's Thesis: " Every effectively calculable function (effectively decidable predicate) is general recursive " (Kleene 1952:300) Turing's Thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

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