1. Turing Machine Implemented In Conway's Game Life, A Download this application, read documentation, and check out thirdparty article discussing various aspects of this kind of research. This is a turing machine implemented in Conway's Game of Life. http://www.rendell.uk.co/gol/tm.htm

2. Turing Machine Article on turing machines from the Stanford Encyclopedia.Category Science Math History People Turing, Alan Mathison......turing machine. A turing machine is an abstract representation ofa computing device. It consists of a read/write head that scans http://plato.stanford.edu/entries/turing-machine/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised FEB 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that mental states just are functional states of a probabilistic automaton, in which binary inputs and outputs have been replaced by sensory inputs and motor outputs.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", Proceedings of the London Mathematical Soceity , Series 2, Volume 42, 1936; reprinted in M. David (ed.)

3. Computing Machinery And Intelligence - A.m. Turing, 1950 What is a turing machine? A turing machine is an automaton which moves along a linear strip of data and performs certain actions according its state, which depends upon the data it has 'seen ' and the datum symbol that it is viewing. http://www.abelard.org/turpap/turpap.htm

[VOL. LIX. No.236.] [October, 1950] MIND A QUARTERLY REVIEW OF PSYCHOLOGY AND PHILOSOPHY Index 1 The Imitation Game 2 Critique of the New Problem 3 The Machine concerned in the Game 4 Digital Computers ... 5 Universality of Digital Computers 6 Contrary Views on the Main Question (1) The Theological Objection (2) The 'Heads in the Sand' Objection (3) The Mathematical Objection (4) The Argument from Consciousness ... Foot notes 1 - COMPUTING MACHINERY AND INTELLIGENCE BY A.M.TURING 1 The Imitation Game I PROPOSE to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine 'and 'think'. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words 'machine' and 'think 'are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, 'Can machines think?' is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described' in terms of a game which we call the 'imitation game'. It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either 'X is A and Y is B' or 'X is B and Y is A'. The interrogator is allowed to put questions to A and B thus:

4. Turing's World: More Information (1) it can be computed by a turing machine. A turing machine is a very simple machine, but, logically speaking, has all the http://www-csli.stanford.edu/hp/Turing1.html

Back Forward Turing Machines Introduced by Alan Turing in 1936, Turing machines are one of the key abstractions used in modern computability theory, the study of what computers can and cannot do. A Turing machine is a particularly simple kind of computer, one whose operations are limited to reading and writing symbols on a tape, or moving along the tape to the left or right. The tape is marked off into squares, each of which can be filled with at most one symbol. At any given point in its operation, the Turing machine can only read or write on one of these squares, the square located directly below its "read/write" head. In Turing's World the tape is represented by a narrow window that sits at the bottom of the screen. Here is what the tape looks like with a series of A's and B's written on it, and with the read/write head located on the leftmost of these symbols. A Turing machine has a finite number of states and is in exactly one of these states at any given time. Associated with these states are instructions telling the machine what action to perform if it is currently scanning a particular symbol, and what state to go into after performing this action. The states of a Turing machine are generally represented by a flow or state diagram, using circles for the states and labelled arcs for the instructions associated with those states. Here, for example, is a state diagram of a Turing machine with two states. When it is in state looking at an A, this machine will move right one square and return to state 0. When it is in state scanning a B, it will change this symbol to an A and go into state 1.

5. Virtual Turing Machine 2.02 Simulates 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).

6. Turing Machine -- From MathWorld serve as an idealized model for mathematical calculation. A turing machine consists of a line of cells known as a "tape" http://mathworld.wolfram.com/TuringMachine.html

Discrete Mathematics Computational Systems Discrete Mathematics Computer Science ... Theory of Computation Turing Machine A theoretical computing machine invented by Alan Turing The number of n -state s -color Turing machines (disallowing machines with halting states) is given by (Wolfram 2002, p. 888). An example 3-state 2-color Turing machine is illustrated above (Wolfram 2002, p. 78). It has a total of rules, which describe the machine behavior for all possible states. In general, an n -state k -color Turing machine requires rules to specify its behavior. Although any number of these rules may specify a halting condition, the most commonly considered Turing machines have either or 1 halting states. A Turing machine can run forever, enter a loop, or reach a particular state or set of conditions (i.e., the head will ever reach a given position, a given pattern will be produced on the tape, etc.) at which it is prescribed to halt. Determining whether a Turing machine will ever halt for a given input and set of rules, is called the halting problem . An n -state, 2-symbol

7. 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 ... Sources Last Update 24 February, 2001

8. Virtual Turing Machine Virtual turing machine (VTM). Virtual turing machine 2. It's better. The sourcecode is prettier. What is a turing machine? Alan Turing was a cryptographer. http://www.nmia.com/~soki/turing/

Virtual Turing Machine (VTM) Virtual Turing Machine 2 It's better. It can detect some infinite loops. The source code is prettier. What is a Turing Machine? Alan Turing was a cryptographer. He helped Britain break the German Enigma machines in WWII. He also invented a concept of a type of computer, called a "Turing Machine." Theoretically, a Turing machine is just as powerful as any other computer. Conceptually, a Turing Machine has a finite set of states, a finite alphabet (that has a blank symbol), and a finite set of instructions. Physically, it has a head that can read, write, and move along an infinitely long tape that is divided into cells, where each cell has a value of blank or a letter in the Turing Machine's alphabet. An instruction is defined as a five tuple, like this: (starting state, starting value, new state, new value, movement) The starting state is the state the head is currently in. The starting value is the value of the cell the head is positioned at. The new state and new value replace the starting state and starting value, respectively. The movement specifies which direction the head moves by one cell. The head halts when it can not find an instruction for the current state or the current cell value. A Turing machine will start at the first non-blank cell. Usually, states are named s

9. Virtual Turing Machine Virtual turing machine. VTM homepage The Tape Blank characterInitial state Instructions This is a small script for adding http://www.nmia.com/~soki/turing/addition.html

Virtual Turing Machine VTM homepage The Tape: Blank character: Initial state: Instructions: # This is a small script for adding two numbers that are # represented by a string of 1s with a length of one more # than the number. The numbers have a single zero # seperating them and a blank at the end. # # Example: 'B11011B' will add 1 + 1 and hopefully get # 'B111BBBB'. # # Try changing the initial tape to watch it work. pass, 1, pass, 1, R # get past the numbers pass, 0, pass, 1, R # change the zero pass, B, del1, B, L # end of second number, start going # back to delete the last 1 del1, 1, del2, B, L # delete the last 1, go back to # delete the second to last 1 del2, 1, stop, B, R # deletes the second to last 1 I want to: execute this script and output: the result of the tape only one line per step two lines per step don't show the state show the state before the tape show the state after the tape and don't show the form again and show the form before the results and show the form after the results save this script with the values VTM homepage

10. Alan Turing - Home Page a concept of a type of computer, called a "turing machine.". Theoretically, a turing machine is just as powerful as any http://www.turing.org.uk/turing

The Alan Turing Home Page Maintained by Andrew Hodges, author of Alan Turing: the Enigma. Quick Links: This page is the guide to a large website dedicated to Alan Turing (1912-1954) Who was Alan Turing? Founder of computer science, mathematician, philosopher, codebreaker, strange visionary and a gay man before his time: 1912 (23 June): Birth, Paddington, London 1926-31: Sherborne School 1930: Death of friend Christopher Morcom 1931-34: Undergraduate at King's College, Cambridge University 1932-35: Quantum mechanics, probability, logic 1935: Elected fellow of King's College, Cambridge 1936: The Turing machine, computability, universal machine 1936-38: Princeton University. Ph.D. Logic, algebra, number theory 1938-39: Return to Cambridge. Introduced to German Enigma cipher machine 1939-40: The Bombe, machine for Enigma decryption 1939-42: Breaking of U-boat Enigma, saving battle of the Atlantic 1943-45: Chief Anglo-American crypto consultant. Electronic work. 1945: National Physical Laboratory, London 1946: Computer and software design leading the world.

11. Alan Turing Scrapbook - Turing Machines s and Simulations OnLine.......The Alan Turing Internet Scrapbook. Computable Numbers, 1936 and the TuringMachine. Other 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 doesn't tell you anything about that completely rewrote the agenda in the foundations of mathematics. This is just mentioned at the end of a worthwhile MacTutor summary of the Beginnings of Set Theory.

12. JavaScript Turing Machines Andrew Hodges, 1 January 2003. The turing machine table of behaviour will appearbelow, set out in quintuples state read write move nextstate. 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.

13. Details Of A Turing Machine In Conway's Game Of Life Details of a turing machine in Conway's Game of Life. Below is a listof the parts with links between. turing machine Parts. 1GAP3. http://www.rendell.uk.co/gol/tmdetails.htm

14. Some Brainfuck Fluff By Daniel B. Cristofani. BF sources for several utility and application programs including a Universal turing machine, BF to SPARC compiler. http://www.hevanet.com/cristofd/brainfuck/

some brainfuck fluff by daniel b cristofani The Epistle to the Implementors please read this before implementing brainfuck. fib.b , which outputs arbitrarily large fibonacci numbers rot13.b , the simplest brainfuck rot13 I've seen (not very concise, more a template than a program) random.b , a random number generator based on a cellular automaton random2.b , alternate output format ("11011100...") move.b , a novel way of moving to the 9999th cell dquine.b , a quine (portable but not that short) dbfi.b , a brainfuck interpreter in brainfuck dbf2c.b , a brainfuck-to-C translator in brainfuck numwarp.b , a number...obfuscator? Prettifier? Dunno. (I haven't seen this transform done before, that I recall.) utm.b , a universal Turing machine wc.b , the standard (line and) word (and character) count utility short.b , an assortment of tiny programs Brief explanatory comments on most of the above programs results0.txt , results of Brainfuck Golf contest results1.txt , results of Brainfuck Golf contest 1 results2.txt , results of Brainfuck Golf contest 2 dbc.c

15. Busy Beaver Turing Machine Busy Beaver turing machine. This story starts around 1960. Tibor Rado,a professor Jeffrey Shallit. turing machine Information. For a http://grail.cba.csuohio.edu/~somos/bb.html

Busy Beaver Turing Machine This story starts around 1960. Tibor Rado, a professor at the Ohio State University, thought of a simple non-computable function besides the standard halting problem for Turing machines. Given a fixed finite number of symbols and states, select those Turing machine programs which eventually halt when run with a blank tape. Among these programs find the maximum number of non-blank symbols left on the tape when they halt. Alternatively, find the maximum number of time steps before halting. This function is well-defined but rapidly becomes un-computable for even a small number of states and symbols. He published an article about it in 1962, but went beyond just writing about a theoretical result. With his student Shen Lin, they actually tackled the two symbol, three state problem. The study resulted in a dissertation for Lin in 1963 and an article in JACM in 1965. After the initial flurry of articles there has been several others mentioning results. The most popular is probably the August 1984 Scientific American Computer Recreations column by Dewdney. There is a PostScript handout by Jeffrey Shallit about the problem.

16. Busy Beaver Turing Machine Fivestate Busy Beaver turing machine Contender. In December, George Uhing of Bronx,NY, found a five-state turing machine that prints 1,915 1's before halting. http://grail.cba.csuohio.edu/~somos/busy.html

Busy Beaver From: csaamw@urc.tue.nl (Michiel Wijers) Date: 6 Jan 1995 10:05:09 GMT Organization: Eindhoven University of Technology, The Netherlands Newsgroups: sci.math Re: Busy Beaver Armando Barbot Matos and Jose Paulo Leal of the Universidade do Porto, Portugal, asked on January 5th in newsgroup Five-state Busy Beaver Turing Machine Contender Scientific American, April 1985 page 30, A.K.Dewdney At the end of the March column I mentioned a new candidate for the five-state busy beaver [see "Computer Recreations," Scientific American; August 1984]. In December, George Uhing of Bronx, N.Y., found a five-state Turing machine that prints 1,915 1's before halting. The Uhing machine is reproduced in the table below. To discover what the machine will do in state B, for example, examine the row bearing that label. The row is subdivided into an upper and a lower portion listing the machine's responses to a or 1 respectively. If the machine reads a 1 on its tape, it enters state D, prints a on the tape and then moves one cell to the left. In the table H means that the machine halts. Uhing, who programs for a Manhattan optical company, decided to search for the five-state busy beaver after reading this column last August. He used a Z-80 microprocessor running an assembly-language program to oversee a second machine: A Turing-machine simulator that cost Uhing less than $100 to build. It goes through seven million Turing-machine transitions per second. Each transition amounts to a simple lookup in a table like the one below. Uhing seems determined to find the five-state busy beaver. Does the present machine qualify? It showed up after Uhing's computer had been running for a month. As far as I know it is still running.

17. Home Page - Hypercomputation Research Network (http://hypercomputation.net) The study of computation beyond that defined by the turing machine, also known as superTuring, non-standard or non-recursive computation. Links to people, resources and discussions. http://www.hypercomputation.net/

HYPERCOMPUTATION.NET Hypercomputation Research Network 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. Jack Copeland has produced some excellent explanatory material which you may find useful: AlanTuring.Net Hypercomputation Page The confusion of Thesis M with the Church-Turing thesis If you would like to comment on any aspect of this site, please email the webmaster People If you wish to be added to our published list of active researchers , please send us your details. Bibliography If you publish or come across any books, articles or papers that you feel may be relevant to researchers in hypercomputation, please send us the details for inclusion in our comprehensive bibliography Discussion If you are active in the field and wish to be involved in discussions relating to it, you may benefit from joining the

18. Turing Machines Category Science. A description of the turing machine and two other systemscapable of universal computation. The original turing machine. http://cgi.student.nada.kth.se/cgi-bin/d95-aeh/get/umeng

19. Programming Turing Machines Programming a turing machine is hard, and there is little or no possibilityof abstraction, making it very hard to implement complex functions. http://cgi.student.nada.kth.se/cgi-bin/d95-aeh/get/umexeng

20. Turing Machine Simulator -- Intro turing machine Simulator Intro. You'll probably want to read some or allof these help files first, though What the heck is a turing machine? http://www.igs.net/~tril/tm/

Turing Machine Simulator Intro The TM Simulator is my first substantial applet, a project I worked on over the summer to help me learn the language, to pass ample free time, and to have fun. It turned out to be alot more difficult than I'd expected, particularly the GUI layout aspects, but I've finally completed enough of it to make it available for public viewing, and in the process I've become moderately proficient at the non-bells-and-whistles aspects of Java. It seems to be working pretty well on the platforms where I've tested it, but if you run into any bugs, please report them to me by email I don't expect this program will be wildly popular with the general public, as it is not replete with cool animation, sound clips, etc....but other theoretical comp sci. geek-types out there might find it a fun toy. So, without further ado, here's a link to the applet itself . You'll probably want to read some or all of these help files first, though: What the heck is a Turing Machine? Using the interface ... The (not-yet-well-documented) source code I've collected some Turing Machine-related links on my Links page.

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