1. Turing Machines Article on turing machines from the Stanford Encyclopedia. http://plato.stanford.edu/entries/turing-machine/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change NOV The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free Turing Machines Turing machines, first described by Alan Turing in (Turing 1937), are simple abstract computational devices intended to help investigate the extent and limitations of what can be computed. Turing, writing before the invention of the modern digital computer, was interested in the question of what it means to be computable. Intuitively a task is computable if one can specify a sequence of instructions which when followed will result in the completion of the task. Such a set of instructions is called an effective procedure , or algorithm , for the task. This intuition must be made precise by defining the capabilities of the device that is to carry out the instructions. Devices with different capabilities may be able to complete different instruction sets, and therefore may result in different classes of computable tasks (see the entry on computability and complexity Turing proposed a class of devices that came to be known as Turing machines. These devices lead to a formal notion of computation that we will call

2. Turing Machines And Universes Essay exploring turing machine theory from quantum mechanical and universal perspectives. http://samvak.tripod.com/turing.html

Turing Machines and Universes By: Dr. Sam Vaknin Malignant Self Love - Buy the Book - Click HERE!!! Relationships with Abusive Narcissists - Buy the e-Books - Click HERE!!! The Web Sam Vaknin Sites READ THIS: Scroll down to review a complete list of the articles - Click on the blue-coloured text! Bookmark this Page - and SHARE IT with Others! In 1936 an American (Alonzo Church) and a Briton (Alan M. Turing) published independently (as is often the coincidence in science) the basics of a new branch in Mathematics (and logic): computability or recursive functions (later to be developed into Automata Theory). The authors confined themselves to dealing with computations which involved "effective" or "mechanical" methods for finding results (which could also be expressed as solutions (values) to formulae). These methods were so called because they could, in principle, be performed by simple machines (or human-computers or human-calculators, to use Turing's unfortunate phrases). The emphasis was on finiteness: a finite number of instructions, a finite number of symbols in each instruction, a finite number of steps to the result. This is why these methods were usable by humans without the aid of an apparatus (with the exception of pencil and paper as memory aids). Moreover: no insight or ingenuity were allowed to "interfere" or to be part of the solution seeking process. No one succeeded to prove that a function must be recursive in order to be effectively calculable. This is (as Post noted) a "working hypothesis" supported by overwhelming evidence. We don't know of any effectively calculable function which is not recursive, by designing new TMs from existing ones we can obtain new effectively calculable functions from existing ones and TM computability stars in every attempt to understand effective calculability (or these attempts are reducible or equivalent to TM computable functions).

3. Virtual Turing Machine 2.02 Simulation of a turing machine. Users can write their own turing machines and see their machines work. http://www.nmt.edu/~prcm/turing/

Virtual Turing Machine 2 (VTM2) The VTM2 distribution (with the command line version and the web version) Grab vtm-2.02.tar.gz . The documentation is ugly. Anybody want to write something better? VTM2 features: a command line interface #! style scripts for UNIX a WWW interface "infinite" tape detection of some infinite loops What is a Turing machine? A Turing machine is theoretical computer consisting of a finite set of internal states, a finite alphabet that includes a blank symbol, and a finite set of instructions. It has a physical head and a physical infinitely long tape, which is divided into cells. The cell values consist of the alphabet. The tape has a finite number of non-blank cells. The head can read and write to the cells and move the tape one cell to the left and one cell to the right. An instruction is defined as a five tuple: (initial state, read value, final state, write value, movement) The inital state is the current internal state of the machine. The read value is the value of the cell the head is currently positioned at. The final state becomes the new state of the machine. The write value overwrites the cell the head is positioned at. Movement specifies which direction the head moves, either left or right. When the machine does not have an instruction for a given internal state and cell value, it will halt. Also, the web version of the VTM2 will halt if the head goes past either end of the tape. The Turing machine will start at the leftmost non-blank cell on the tape (if there are no non-blank cells in the tape, the VTM will start in the middle of the tape).

4. Turing Machine of a turing machine Computation......Figure 3 The Instantaneous http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Turing Machine More results from plato.stanford.edu turing machine Wikipedia, the free encyclopediaThe concept of the turing machine is based on the idea of a person executing A turing machine is a pushdown automaton made more powerful by relaxing the http://plato.stanford.edu/archives/sum2003/entries/turing-machine/

This is a file in the archives of the Stanford Encyclopedia of Philosophy version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses HTML 4/Unicode to display special characters. Older browsers and/or operating systems may not display these characters correctly. last substantive content change MAY Turing Machine History Later Developments Bibliography Other Internet Resources ... Related Entries History Turing machines were first proposed by Alan Turing, in an attempt to give a mathematically precise definition of "algorithm" or "mechanical procedure". Early work by Turing and Alonzo Church spawned the branch of mathematical logic now known as recursive function theory. Later Developments The concept of a Turing machine has played an important role in the recent philosophy of mind. The suggestion has been made that mental states just are functional states of a probabilistic automaton, in which binary inputs and outputs have been replaced by sensory inputs and motor outputs. This idea underlies the theory of mind known as "machine functionalism". Bibliography Turing, A., "On Computable Numbers, With an Application to the Entscheidungsproblem"

6. The Church-Turing Thesis All computable functions are computable by turing machine. Corollaries such as the following are sometimes offered http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Turing Machine - Wikipedia, The Free Encyclopedia The concept of the turing machine is based on the idea of a person A turing machine that is able to simulate any other turing machine is called a http://en.wikipedia.org/wiki/Universal_Turing_machine

8. Turing Machines As we might phrase their common definition now A function is computable if it can be computed by a turing machine. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. JavaScript Turing Machines turing machines, formulated by Alan Turing in 1936 as the foundation of computability and modern computers. http://www.turing.org.uk/turing/scrapbook/tmjava.html

The Alan Turing Internet Scrapbook Turing Machines implemented in JavaScript maintained by Andrew Hodges Alan Turing home page Scrapbook index ... My Books Turing machines implemented in JavaScript Here you can see the basic ideas of Turing machines illustrated by some very simple examples. Continue to the Scrapbook page on Alan Turing and his Turing machines for more general information on the machine concept. CLICK on one of these: Machine 1: unary addition Machine 2: divisibility Machine 3: primality The tape will appear here. The scanned square, marked off with , remains fixed while the tape passes through it. Current state number Current tape position Current step number What to do: First choose your machine by CLICKing on the selection. Then click on LOAD. Now you can choose STEP to make the machine take one step at a time, or RUN to let the machine run until it terminates the calculation. You can interrupt a RUN with BREAK. To resume, click on CONTINUE and then either STEP or RUN. Reset by using LOAD. The machines: Machine 1 is there to illustrate the basic operations. Step through the moves to see how it 'adds' two groups of 1's into a single group.

10. Turing Machine - Wikipedia, The Free Encyclopedia Wikipedia article. http://en.wikipedia.org/wiki/Turing_machine

Turing machine From Wikipedia, the free encyclopedia. The Turing machine is an abstract machine introduced in by Alan Turing to give a mathematically precise definition of algorithm or 'mechanical procedure'. The concept is still widely used in theoretical computer science , especially in complexity theory and the theory of computation . The thesis that states that Turing machines indeed capture the informal notion of effective or mechanical method in logic and mathematics is known as the Church-Turing thesis The concept of the Turing machine is based on the idea of a person executing a well-defined procedure by changing the contents of an infinite number of ordered paper sheets that can contain one of a finite set of symbols. The person needs to remember one of a finite set of states and the procedure is formulated in very basic steps in the form of "If your state is 42 and the symbol you see is a '0' then replace this with a '1', remember the state 17, and go to the following sheet.". Turing machines shouldn't be confused with the Turing test , Turing's attempt to capture the notion of artificial intelligence A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine or simply a universal machine as Turing described it in 1947: It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called the universal machine.

11. JavaScript Turing Machines The turing machine table of behaviour will appear below, set out in quintuples state read write move nextstate http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Alan Turing Scrapbook - Turing Machines The turing machine concept involves specifying a very restricted set of logical What s more it was essential to Turing s 1936 work that a turing machine http://www.turing.org.uk/turing/scrapbook/machine.html

The Alan Turing Internet Scrapbook Computable Numbers, 1936 and the Turing Machine Quick Links: Boy to Man... The years from 1932 to 1935 were the foundation of Alan Turing's serious scientific life. The atmosphere at King's College, Cambridge, was highly conducive to free-ranging thought, and it was as an undergraduate there that Alan Turing developed the inspiration he had received from Christopher Morcom, and combined it with the newest ideas in mathematics. On-line extract from my book on the moral and political ambience at King's College, and Alan Turing's life and thought in 1933. ...Man to Machine Mathematical Logic In 1935 a course by the Cambridge mathematician M. H. A. (Max) Newman introduced Alan Turing to the frontier of research in mathematical logic. Logic is not well represented on the Web, and unfortunately the Beginnings of Set Theory. This Encyclopaedia Britannica article on Logic discusses the background to decidability in mathematical logic. The famous 1900 speech by the German mathematician David Hilbert did much to set the agenda for twentieth century mathematical research. More comment

13. Alan Turing - Home Page logic 1935 Elected fellow of King's College, Cambridge 1936 The turing machine, computability, universal machine 193638 Princeton http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Turing Machine -- From MathWorld A turing machine consists of a line of cells known as a tape that can be An example 3state, 2-color turing machine is illustrated above (Wolfram 2002 http://mathworld.wolfram.com/TuringMachine.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Discrete Mathematics Computational Systems Discrete Mathematics ... Commands Turing Machine A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a line of cells known as a "tape" that can be moved back and forth, an active element known as the "head" that possesses a property known as "state" and that can change the property known as "color" of the active cell underneath it, and a set of instructions for how the head should modify the active cell and move the tape (Wolfram 2002, pp. -81). At each step, the machine may modify the color of the active cell, change the state of the head, and then move the tape one unit to the left or right. Turing machines will be implemented in a future version of Mathematica as TuringMachine A generalization of the Turing machine in which the head is allowed to move steps in either direction was considered by Macura (2005).

15. Turing Honoured With Bronze Statue The Register Alan Turing was one of the Great Ones of Computing. In the 1930's he developed the concept of a turing machine, arguably the basis of modern http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. Universal Turing Machine -- From MathWorld A turing machine which, by appropriate programming using a finite length of Upon conversion to a 2color machine, Minsky s universal turing machine http://mathworld.wolfram.com/UniversalTuringMachine.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Discrete Mathematics Computer Science Theory of Computation ... Unsolved Problems Universal Turing Machine A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave the first construction for a universal Turing machine (Turing 1937, 1938). Shannon (1956) showed that two colors were sufficient, so long as enough states were used. Minsky (1962) discovered a 7-state 4-color universal Turing machine, illustrated above (Wolfram 2002, p. ). Note that the 20th rule specifies that the Turing machine should halt, as indicated by leaving the head stationary and not changing its state. Upon conversion to a 2-color machine, Minsky's universal Turing machine requires 43 states. Comparatively little more was published about small universal Turing machines until Rogozhin (1996) found examples with the numbers of states and colors given by (24, 2), (10, 3), (7, 4), (5, 5), (4, 6), (3, 10), and (2, 18) (Wolfram 2002, p.

17. Introduction To Cellular Automata (game of life, brian's brain ) available in PDF, illustrated with a program (CAV) and an applet which show the capability of a conway CA to manage boolean functions as part of a turing machine(LogiCell). http://www.rennard.org/alife/english/acgb.html

Introduction to Cellular Automata Cellular Automata Viewer CAV is a cellular automata manager. Version 2.0 Small but complete, it will allow you to explore Conway's universe (the famous Game of Life) as well as more complex and sophisticated universes (Brian's Brain, Swirl...). Version 2.0 implements some 1D cellular automata. Logicell LogiCell is an applet which demonstrates the capability of a Conway Cellular Automaton to manage boolean operators. It is illustrated with some automatism applications (binary adder, two-way switch...). H ome Cellular Automata Biomorphs ... Links Last Update 5 December, 2004

18. Virtual Turing Machine A web based turing machine. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Turing Machine Simulator Home Worlds Apart GtkLife Scrabble Challenge Costa Rica Fvwm Turing Contact Site Updated 2005/January/13 http://ironphoenix.org/tril/tm/

You need a Java-enabled browser to run this program. Instructions Source Code Home Worlds Apart ... Site Updated : 2005/January/13 the credits before you borrow any of the graphics on these pages.

20. Computing Machinery And Intelligence - A.m. Turing, 1950 The classic 1950 article by Alan Turing on machine intelligence, where he introduces the famous Turing test. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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