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# Topic: Turing completeness

 Turing completeness - Wikipedia, the free encyclopedia In computability theory, an abstract machine or programming language is called Turing complete, Turing equivalent, or (computationally) universal if it has a computational power equivalent to a universal Turing machine (a simplified model of a programmable computer). Turing completeness is significant in that every plausible design for a computing device so far advanced can be emulated by a universal Turing machine. The computational systems (algebras, calculi) that are discussed as Turing complete systems are those intended for studying theoretical computer science. en.wikipedia.org /wiki/Turing_completeness   (900 words)

 Turing machine - Wikipedia, the free encyclopedia Turing machines are extremely basic symbol-manipulating devices which — despite their simplicity — can be adapted to simulate the logic of any computer that could possibly be constructed. Turing completeness, an attribute used in computability theory to describe computing systems with power equivalent to a universal Turing machine. Turing tarpit, any computing system or language which, despite possessing Turing completeness, is generally considered useless for practical computing. en.wikipedia.org /wiki/Turing_machine   (3442 words)

 BF is Turing-complete Turing Machine, a very simplistic computing model, which yet is powerfull enough to calculate all possible function which can be calculated. A Turing Machine consists of an endless tape of cells, which each can contain any of a given set of symbols, a pointer pointing to one of the cells, and a certain finite state control. To simulate a Turing machine, we need an array with unlimited length to represent the tape, a index into that array representing the position of the head, and the current state. www.iwriteiam.nl /Ha_bf_Turing.html   (1671 words)

 Turing completeness: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-12) The turing machine is an abstract machine introduced in 1936 by alan turing to give a mathematically precise definition of algorithm or mechanical... (Turing completeness is often loosely attributed to physical machines or programming languages that would be universal if they had indefinitely enlargeable storage and were absolutely reliable. Turing completeness is significant in that every plausible design for a computing device so far advanced (even quantum computer quantum computer quick summary: www.absoluteastronomy.com /encyclopedia/t/tu/turing_completeness.htm   (2071 words)

 EECS290n Lecture 17 Notes   (Site not responding. Last check: 2007-10-12) Each actor by itself is a finite state machine, that does not imply Turing completeness. Therefore it can't be the actors and the values, it must be the buffers to fulfill Turing completeness. A Kahn-McQueen network therefore is Turing Complete, the halting problem (the deadlock problem) is not decidable for the whole class. ptolemy.eecs.berkeley.edu /~eal/ee290n/lec18.scribe.html   (509 words)

 Preface   (Site not responding. Last check: 2007-10-12) This discrete theory is based on the Turing machine model and achieves a classification of discrete computational problems according to their algorithmic difficulty. Turing machines formalize algorithms which operate on finite strings of symbols over a finite alphabet. While the part of his theory based on the Turing approach (#P-completeness) is now standard and well-known among the theoretical computer science community, his algebraic completeness result for the permanents received much less attention. math-www.uni-paderborn.de /~pbuerg/agpb/publications/preface-habil.html   (840 words)

 Turing tarpit - Esolang A Turing tarpit is a language that aims for Turing-completeness in an arbitrarily small number of linguistic elements - ideally, as few as possible. The reader is welcome to enter the competition [to design the smallest universal Turing machine...] although the reader should understand clearly that the question is an intensely tricky puzzle and has essentially no serious mathematical interest. The pursuit of Turing tarpits in the esoteric programming language community, however, seems to be essentially for its own sake. esoteric.voxelperfect.net /wiki/Turing_tarpit   (546 words)

 [No title] Daniel B Cristofani (cristofdathevanetdotcom) http://www.hevanet.com/cristofd/brainfuck/ This Turing machine achieves Turing-completeness not by simulating other Turing machines directly, but by simulating a Turing-complete class of tag-systems (a computational model invented by Emil Post and named after the children's game "tag"). The brainfuck cells representing the Turing machine cells are laid out contiguously from the beginning of the tape, except that the head of the Turing machine is represented by a gap of three brainfuck cells, just to the left of the brainfuck cell that represents the current Turing machine cell. At the start of each cycle, the rightmost of these three cells holds the Turing machine state, where states 1-4 are represented by 1-4 and "halt" (here treated as a separate state) is represented by 0. www.hevanet.com /cristofd/brainfuck/utm.b   (1487 words)

 Computabilty and Completeness Within the classical framework, the most important limit on what can be computed by a Turing Machine is completeness, or halting, two manifestations of the same underlying structural feature of algorithmic computation. The general problem of incompleteness, of which Gödel's (1931) famous theorem and Turing's (1936) halting problem are symptoms, is straightforward: within a formal system with a given algorithmic information content, we cannot prove any theorem with an information content exceeding that of the formal system by more than a fixed number of bits. But this contradicts Turing's theorem that there can be no effective procedure for determining the halting status of an arbitrary program. www.mulhauser.net /research/tutorials/computability/completeness.html   (1180 words)

 The Origins of the Turing Thesis Myth | Lambda the Ultimate Turing Thesis: Whenever there is an effective method (algorithm) for obtaining the values of a mathematical function, the function can be computed by a TM. After all, if one goes back to the definition of the Turing machine, its computation is nothing more than a series of lookups in a transition table, and it could be viewed as a sequence of computations by a finite automaton. Most of practical PLs are "Turing complete" (can compute any "compute" function), but are not limited to just functions (mostly because of their support for interaction). lambda-the-ultimate.org /node/view/203   (1644 words)

 Coherence Engine: June 2003 Now, again, this is not to dismiss the importance of the Turing Machine, its relevance as a model of computation, or the intellectual achievement of Alan Turing in showing the limits of mechanical, embodied, computation. Keep this in mind: Turing's accomplishment was not showing the universality of the machine, although he did do that; it was in showing the fundamental limits of it. Turing didn't prove the universality of the Turing Machine; he proved that a) a single Universal Turing Machine can simulate all other Turing Machines and b) the Turing Machine model was equivalent to a number of mechanical algorithms for solving problems. www.coherenceengine.com /blog/2003_06_01_archive.html   (4752 words)

 A Simple Proof for the Turing-Completeness of XSLT and XQuery Since computation with Turing machines is the most powerful model of computation known to exist, Turing-completeness of a language basically means that everything that can be computed at all can be computed with implementations of the language. After completion of the called template execution of the calling template is continued, as is standard for procedure calls. Completeness of the translation is simply given by the fact that we provide a translation that follows the structural definition of μ-recursive functions. www.mulberrytech.com /Extreme/Proceedings/html/2004/Kepser01/EML2004Kepser01.html   (6730 words)

 LtU Classic Archives Turing completeness is oriented towards functions from input to output, while more or less ignoring interaction, time, trust, fairness. Daniel Yokomizo - Re: Turing completeness is not? Marc Hamann - Re: Turing completeness is not? lambda-the-ultimate.org /classic/message12481.html   (1862 words)

 Comments on 14482 | Ask MetaFilter   (Site not responding. Last check: 2007-10-12) Now, the neat thing is that a Turing Machine is one of the things that can be "calculated", which is to say, a Turing Machine can be programmed to simulate a Turing Machine. Turing machines don't directly support the first, for instance, and the lambda calculus doesn't support any of the requirements directly. Oh, and by the way, Postscript and TeX are both turing complete, in case someone wants to use text formatting languages to solve the worlds problems. ask.metafilter.com /mefi/14482   (2650 words)

 Turing - TheBestLinks.com - Alan Turing, Computer, Computer science, Church-Turing thesis, ...   (Site not responding. Last check: 2007-10-12) Turing machine and Turing completeness, an abstract model of computer execution and storage. Turing test, a proposal for a test of a machine's capability to perform human-like conversation. Turing Award, sometimes called the "Nobel Prize of computing". www.thebestlinks.com /Turing.html   (137 words)

 ILovePhilosophy.com Discussion Forums :: View topic - Snow Crash - 'Information Hygiene' Turing completeness is the definition of a computer. The Turing machine, developed by Alan Turing in the 1930s, consists of tape of unlimited length that is divided into little squares. Well, in a quantum Turing machine, the difference is that the tape exists in a quantum state, as does the read-write head. www.ilovephilosophy.com /phpbb/viewtopic.php?t=139373&start=40   (7158 words)

 URCS Theory Technical Reports Despite the fact that we prove query-increasing and query-decreasing Turing reductions to in the general case be strictly weaker than Turing reductions, we identify a broad class of sets A for which any set that Turing reduces to A will also reduce to A via both query-increasing and query-decreasing Turing reductions. We completely determine the relative power of the different models of witness-isomorphic reduction, and we show that witness-isomorphic reductions can be used in a uniform approach to the local search problem. Complete characterizations in terms of well-known complexity classes are given for the classes of languages recognized by polynom www.cs.rochester.edu /trs/theory-trs.html   (16132 words)

 [No title] Even today, if you browse the books on C++ in your local bookstore, you'll find dozens of chapters on fancy structs and maybe a short section in the miscellaneous chapter at the end on templates. With the addition of templates the compiler itself becomes Turing complete. While the C preprocessor can be proved not to be Turing complete the C++ compiler can actually perform important work at compile time lightening the load at runtime. homepage.mac.com /sigfpe/Computing/peano.html   (778 words)

 [No title]   (Site not responding. Last check: 2007-10-12) We will model Turing ; machine's tape by two lists. We will never write out this tail of blanks explicitly; ; rather we will assume that there is always a blank cell after the ; right end of every finite string under re-writing. ; ; For example, a pair of lists ; (2 1 #f) (3) ; stands for a Turing machine configuration with a tape ; containing a blank, followed by a symbol '1' then symbol '2' and then ; symbol '3'. okmij.org /ftp/Scheme/turing-completeness-limited-macros.scm   (509 words)

 Turing completeness - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-12) Languages designed for less common paradigms including functional languages such as LISP and Haskell, and logic programming languages such as Prolog are also Turing-complete. A more powerful but still not Turing complete extension of finite automata are formal languages. One important result from computability theory is that it is impossible in general to find if a program written in a Turing-complete language will continue executing forever or will stop within a finite period of time (see halting problem). www.mywikipedia.us /Turing-complete   (590 words)

 Complexity & Information Theory One of many interesting features of algorithmic information theory is that it turns out that in the space of all possible strings, hardly any strings can actually be compressed at all. We define the algorithmic information content I(x) of an object (or bit string) x as the length of the shortest self delimiting program(s) for a Universal Turing Machine U which generates a description of that object for a given level of precision. Notice that the choice of a particular U cannot introduce more than O(1) difference in the numerical value of I(x), since any prefix s which makes U simulate another computer is of constant length. www.mulhauser.net /research/tutorials/complexity/complexity.html   (1531 words)

 Alan Turing - Uncyclopedia   (Site not responding. Last check: 2007-10-12) Alan Turing (1923-1949) was a pioneer computer scientist most famous for subtly weaving his deviant homosexual agenda into the basic tenets of computer science, the subliminal influence of which led to the high incidence of homosexuality among computer users that surged exponentially in the 1980s and '90s. He invited young men to sit alone in another room and communicate with him via a teletype terminal, and through typed conversations deduce whether or not he was hard... In his holy quest for a unified theory of computer science, Turing also developed a property called Turing completeness, which is the ability of a given machine or computer language to potentially execute any program imaginable, especially dating sims. uncyclopedia.org /wiki/Alan_Turing   (170 words)

 C++ Template Metaprogramming   (Site not responding. Last check: 2007-10-12) No computers completely meet this requirement, as a Turing machine has unlimited storage capacity, impossible to emulate on a real device. Thus, a machine that can act as a universal Turing machine can, in principle, perform any calculation that any other computer is capable of. In 1966 Bohm and Jacopini proved, that Turing machine implementation is equivalent the exsistence of conditional and looping control structures. www.zolix.hu /ch06s04.html   (826 words)

 [No title] More precisely, a Turing machine consists of: A tape which is divided into cells, one next to the other. The tape is assumed to be arbitrarily extendible to the left and to the right, i.e., the Turing machine is always supplied with as much tape as it needs for its computation. An action table (or transition function) that tells the machine what symbol to write, how to move the head ('L' for one step left, and 'R' for one step right) and what its new state will be, given the symbol it has just read on the tape and the state it is currently in. www.cs.usu.edu /~allanv/cs4700/Loud1.ppt   (1126 words)

 Literature Review: Nature Refutes ID?: The Evolutionary Origin of Complex Features If it is Turing complete then it could have generated in principle the phrase. But if Avida is demonstrably a universal Turing machine, then the set of computable algorithms that can be implemented is large -- so large that any specificity claims about the instruction set is rather unbelievable. After reading GP's post, and after some more thought, I agree that the flexibility of the Lenski system (Turing complete) is indeed a strong point, and is not a "red herring". www.iscid.org /boards/ubb-get_topic-f-18-t-000001-p-17.html   (4075 words)

 John Middlemas So then there is no reason HTML should not progress to turing completeness. Access and editing of the database could also be handled by HTML if it was turing complete. As I understand Turing machines (HTML analogy), you would mainly need the ability to automatically move data between pages, given that the HTML page is the building block (analogy with turing tape placeholder) of the system. www.users.zetnet.co.uk /pld/web/624.htm   (695 words)

 blarg?: Linguisticism I think it's a strong argument, too; if a language is Turing-complete, then in principle anything that you can express in one language you can express in another. The thing is, Turing-completeness (and, I think, completeness proofs in general) makes no mention of how hard or how easy that mapping will be on the programmer. A man may take to drink because he feels himself to be a failure, and then fail all the more completely because he drinks. neon.polkaroo.net /~mhoye/blarg/archives/001782.php   (1127 words)

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