, or cellular automaton is said to be Turing complete if and only if such system can simulate any single taped Turing machine . Classical Turing complete systems include recursive function s and lambda calculus . Named after Alan Turing , in practice Turingcompleteness means that the rules followed ... machine or programming language Turingcompleteness A computational system that can compute every ... streams with infinitely many 1s. Overview Turingcompleteness, named after Alan Turing , is significant ... amounts of working memory, Turingcompleteness is often loosely attributed to physical machines ... s, such as brainfuck . The specific language features used to achieve Turingcompleteness can ... repetition Haskell and Prolog, lacking looping almost entirely, would use recursion . Turingcompleteness ... used to implement that capability. Turingcompleteness in SQL is implemented through proprietary ... cgi wiki?TuringComplete c2.com DEFAULTSORT TuringCompleteness Category Theory of computation Category ...For the usage of this term in the theory of relative computability by oracle machines Turing reduction ... memory memory locations. To show that something is Turing complete, it is enough to show that it can ... sets are Turing complete, notwithstanding finite memory issues. A universal computer is defined as a device with a Turing complete instruction set, infinite memory, and an infinite lifespan. All ... construct. In computability theory, there is a closely related concept known as Turing equivalence. Two computers P and Q are called Turing equivalent if P can simulate Q and Q can simulate P. Thus, a Turing complete system is one that can simulate a Turing machine, but the term is most often used to mean Turing equivalent to a Turing machine. The reason is that any real world computer can be simulated by a Turing machine, an observation codified as the Church Turing thesis . A computer with access to an infinite tape of data is sometimes more powerful than a Turing machine, because the tape ... more details
of completeness. See History of the Church Turing thesis . A formal system is consistency consistent ...Wiktionarypar completeness In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields. Logical completenessCompleteness logic redirects here In logic , semantic completeness is the Conversion logic converse of soundness for formal systems . A formal system is semantically complete when all its tautology logic tautologies are theorem s, whereas a formal system is sound when all theorems are tautologies that is, they are semantically valid formulas formulas that are true under every interpretation of the language of the system that is consistent ... of span style font family cursive,roman S span . This is also called negation completeness . In another ... connective s is functional completeness functionally complete if and only if it can express all ... December 2008 Mathematical completeness In mathematics , complete is a term that takes on specific ... . The completeness of the real numbers is one of the defining properties of the real number system. It may be described equivalently as either the completeness of R as metric space or as a partially ... of zero. See completeness statistics . In graph theory , a complete graph is an undirected graph ... theory and related fields such as lattice order lattice and domain theory , completeness order theory completeness generally refers to the existence of certain supremum suprema or infimum infima .... Computing In algorithms , the notion of completeness refers to the ability of the algorithm ... . In software testing, completeness has for goal the functional verification of call graph between software item and control graph inside each software item . The concept of Completeness knowledge bases completeness is found in knowledge base theory. Economics, finance, and industry Complete market s versus incomplete markets In auditing , completeness is one of the financial statement assertions ... more details
Infobox programming language name Turing logo paradigm Multi paradigm programming language multi paradigm Object oriented programming object oriented , procedural programming procedural , concurrent programming concurrent year 1987 designer Ric Holt and James Cordy developer Ric Holt and James Cordy latest release version X.Y.Z release date mf yes YYYY MM DD latest release date typing static typing static , manifest typing manifest implementations dialects influenced by Concurrent Euclid , Turing programming language Turing influenced Object Oriented Turing operating system license website file ext TuringTuring Plus is a concurrent systems programming language based the Turing programming language designed by James Cordy and Ric Holt , then at the University of Toronto , in 1987. Some, but not all, of the features of Turing were eventually subsumed into Object Oriented Turing . Turing extended original Turing with processes and monitor synchronization monitor s as specified by C.A.R. Hoare as well as language constructs needed for systems programming such as binary input output, separate compilation, variables at absolute addresses, type converters and other features. Turing was explicitly designed to replace Concurrent Euclid programming language Concurrent Euclid in systems programming applications. The TUNIS TUNIS operating system , originally written in Concurrent Euclid, was recoded to Turing in its MiniTunis implementation. Turing has been used to implement several production software systems, including the TXL programming language . References cite book title The Turing Plus Report last1 Holt first1 R C authorlink1 Ric Holt last2 Cordy first2 J R authorlink2 James Cordy edition revised date 1987 09 02 publisher Computer Systems Research Institute, University of Toronto ... the Turing Plus language last1 Holt first1 R C authorlink1 Ric Holt last2 Penny first2 D A year 1988 ... cite book title The concurrent programming of operating systems using the Turing Plus language ... more details
mergeto Completeness of the real numbers discuss Talk Completeness axiom Merger proposal date October 2010 In mathematics the completeness axiom , also called Dedekind completeness of the real numbers, is a fundamental property of the set R of Real number Axiomatic approach real number s. It is the property that distinguishes R from other ordered field s, especially from the set of rational number s. The axiom states that every non empty subset S of R that has an upper bound in R has a least upper bound, or supremum , in R . See the article on Construction of the real numbers Synthetic approach construction of the real numbers for a full explanation. The completeness axiom should not be confused with the topological property of complete metric space Completion completeness of a metric space . The two properties are related, since R , as a metric space with the standard absolute value metric where the distance between x and y is x &minus y , does have the latter property as a consequence of its Dedekind completeness. Indeed, R is the Complete metric space Completion completion , in the sense of metric spaces, of the set Q of rational numbers under the absolute value metric. Thus, the completeness property of metric spaces is one generalization of the completeness axiom itself. Another generalization focuses on the ordering of the real numbers. In any partially ordered set , the analog of Dedekind completeness is the property that every non empty subset that is bounded above has a least upper bound in other words, the same axiom interpreted in greater generality. A partially ordered set with this property is a lattice order lattice , specifically a Lattice order Conditional completeness conditionally complete lattice . In practice a stronger property is usually employed that every subset, whether or not it is empty or bounded above, has a least upper bound. Such a partially ordered set is called a complete lattice . Category Real numbers math stub ... more details
unreferenced date July 2008 Infobox single Wikipedia WikiProject Songs Name My Completeness Cover My completeness.jpg Caption Artist Thirsty Merc from Album Thirsty Merc Label Warner Music Australia Format CD Single , Digital Download Writer Rai Thistlethwayte , Phil Stack Producer Lindsay Gravina Genre Pop rock Released July 26, 2004 Last single Emancipate Myself br 2004 This single My Completeness br 2004 Next single Someday, Someday br 2004 My Completeness was the second single released from Thirsty Merc Thirsty Merc s debut album Thirsty Merc album Thirsty Merc . Reaching number two on the Australian Airplay Chart, the single was the most successful single for the band at the time of its release. It performed considerably better than predecessor, Emancipate Myself , peaking at 27 on the Australian Singles Chart, while highlighting the musical depth and sincerity of the band that secured them a reputation as one of the world s premier alternative acts. Music video The music video features all members of the band in an acoutic setting which is later met by various females surrounding the band filming them with handheld cameras. Additional footage is also taken by the actual handheld cameras seen throughout the video. http www.youtube.com watch?v 7lGdrWotfK8 Track listing My Completeness Dreamer No Sugar Wasting Time Emancipate Myself Chart Positioning class wikitable align left Chart 2004 align left Peak br Position align left Australian ARIA Charts ARIA Singles Chart align center 27 align left Australian Airplay Chart align center 2 align left New Zealand Singles Chart align center 34 References reflist Thirsty Merc Category 2004 singles Category Thirsty Merc songs Category Songs written by Rai Thistlethwayte ... more details
Refimprove date August 2009 In statistics , completeness is a property of a statistic for which the statistic optimally obtains information about the unknown parameters characterizing the distribution of the population, of which a sample appears in the data. It is closely related to statistical sufficiency statistics sufficiency . Definition We consider a random variable X whose probability distribution belongs to a parametric family of probability distributions P sub sub parametrized by . Formally, a statistic s is a measurable function of X thus, a statistic s is evaluated on a random variable X , taking the value s X , which is itself a random variable. A given realization of the random variable X is a data point datum , on which the statistic s takes the value s X . The statistic s is said to be complete for the distribution of X if for every measurable function g the following implication holds E g s X 0 for all implies that P sub sub g s X 0 1 for all . The statistic s is said to be boundedly complete if the implication holds for all bounded g . Example 1 Bernoulli Model This example can be found in. ref Casella, G. and Berger, R. L. 2001 . Statistical Inference. pp. 285 286 . Duxbury Press. ref Let X be a random sample of size n such that each X sub i sub has Bernoulli Distribution with parameter . Let T be the number of 1 s observed in the sample. T is a statistic of X which has Binomial distribution with paramater n , . If the parameter space ... variables associated with P sub sub are all discrete or are all continuous. ref Importance of completeness The notion of completeness has many applications in statistics, particularly in the following two theorems of mathematical statistics. Lehmann Scheff theorem Completeness occurs in the Lehmann ... Completeness occurs in Basu s theorem , ref Casella, G. and Berger, R. L. 2001 . Statistical ... . References references DEFAULTSORT Completeness Statistics Category Statistical theory de Vollst ndigkeit ... more details
that this condition is strictly weaker than functional completeness. ref name Wesselkamper1975a citation ... math . Characterization of functional completeness further Post s lattice Emil Leon Post Emil Post ... complete set. Other meanings Apart from logical connectives Boolean operators , functional completeness ... more details
Turing equivalence may refer to Turingcompleteness , having computational power equivalent to a universal Turing machine Turing degree equivalence of sets , having the same level of unsolvability See Turing machine equivalents . disambig ... more details
Turing may refer to Alan Turing , the British mathematician, logician, cryptanalyst, and computer scientist after whom the items listed below are ultimately named Turing machine , a basic, abstract symbol manipulating device Church Turing thesis , the hypothesis that recursion, calculus, and the Turing machine are of equal computational power Turingcompleteness , a level of computational power of a computational system Turing test , the artificial intelligence test Reverse Turing test Turing Award , the annual computer science award given by the Association for Computing Machinery Turing cipher , a cryptographic stream cipher designed for CDMA Turing programming language , a Pascal based programming language for teaching Turing Number, another term for a CAPTCHA Turing Police, a fictional law enforcement agency in the novel Neuromancer disambig da Turing de Turing el es Turing desambiguaci n fr Turing homonymie gl Turing lt Turing pt Turing ... more details
refimprove article date June 2008 A Turing tarpit is any programming language or computer interface that allows for a great deal of flexibility in function but is difficult to learn and use because it offers little or no support for common tasks. The phrase was coined by Alan Perlis in the epigram quote 54. Beware of the Turing tar pit in which everything is possible but nothing of interest is easy. Alan Perlis Epigrams on Programming ref http www pu.informatik.uni tuebingen.de users klaeren epigrams.html Epigrams on Programming , SIGPLAN Notices Vol. 17, No. 9, September 1982, pages 7 13. ref In any turingcompletenessTuring complete language, it is possible to write any computer program save differences in input output formatting , so in a very rigorous sense nearly all programming languages are equally capable. Turing tarpits prove that theoretical ability is not the same as usefulness in practice. A clear way of measuring this difference is by comparing the average lengths of common programs implemented in different systems. However, a very short version of a program may also be very hard to read. Turing tarpits are characterized by having a simple abstract machine which requires the user to deal with many details in the solution of a problem. At the extreme opposite are interfaces which can perform very complex tasks with little human intervention but become obsolete if requirements change slightly. Some esoteric programming languages , such as Brainfuck , are specifically referred to as Turing tarpits , meaning they purposefully implement a minimum of functionalities to be classified as a Turing complete language. See also Greenspun s Tenth Rule Zawinski s law of software envelopment Turingcompleteness References reflist http www.cs.colorado.edu department publications reports docs CU CS 369 87.pdf G. Fischer, A.C. Lemke Constrained Design Processes Steps Toward Convivial Computing http cleo.ics.uci.edu teaching Winter10 231 readings 1 HutchinsHollanNorman DirectManipulation ... more details
In computability theory , a Turing reduction from a problem A to a problem B , named after Alan Turing ... for solving B . More formally, a Turing reduction is a function computable by an oracle machine with an oracle for B . Turing reductions can be applied to both decision problem s and function problem s. If a Turing reduction of A to B exists then every algorithm for B can be used to produce ... computability, then called relative reducibility, was given by Alan Turing in 1939 in terms ... recursive function recursive function s. In 1944 Emil Post used the term Turing reducibility to refer ..., we say math A math is Turing reducible to math B math and write math A leq T B math if there is an oracle ... enumerable set recursively enumerable and B computably enumerable . We say math A math is Turing ... B leq T A. math The equivalence class es of Turing equivalent sets are called Turing degree s . The Turing ... subseteq mathcal P mathbb N math , a set math A subseteq mathbb N math is called Turing hard for math ... X math then math A math is called Turing complete for math mathcal X math . Relation of Turingcompleteness to computational universality Turingcompleteness, as just defined above, corresponds only partially to Turingcompleteness in the sense of computational universality. Specifically, a Turing machine is a universal Turing machine iff its halting problem i.e., the set of inputs for which ... condition for a machine to be computationally universal, is that the machine s halting problem be Turing ... math denote the set of input values for which the Turing machine with index e halts. Then the sets math A e mid e in W e math and math B e,n mid n in W e math are Turing equivalent here math e,n math ... are not only Turing reductions but many one reductions , discussed below. Properties Every set is Turing equivalent to its complement Every computable set is Turing reducible to every other computable ... math A,B math such that A is not Turing reducible to B and B is not Turing reducible to A . Thus ... more details
date May 2010 At the other extreme, some very simple models turn out to be Turingcompleteness ... Harvard architecture Probabilistic Turing machine Quantum Turing machine Turingcompleteness , an attribute ...two other uses the test of artificial intelligence Turing test the instrumental rock band Turing Machine band turing Image Maquina.png thumb An artistic representation of a Turing machine Rules table not represented A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic ... inside a computer. The Turing machine was described by Alan Turing in 1936, ref The idea came to him ... Hodges 1983 93 . Turing submitted his paper on 31 May 1936 to the London Mathematical Society ... 1937 cf Hodges 1983 129 . ref who called it an a utomatic machine . The Turing machine is not intended ... machine. Turing machines help computer scientists understand the limits of mechanical computation. Turing gave a succinct definition of the experiment in his 1948 essay, Intelligent Machinery . Referring to his 1936 publication, Turing wrote that the Turing machine, here called a Logical Computing ... eventually have an innings. ref See the definition of wikt innings innings on Wiktionary ref Turing 1948, p. 61 blockquote A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine UTM , or simply a universal machine . A more mathematically oriented definition ... intertwined with Turing s in a formal theory of computation known as the Church Turing thesis . The thesis states that Turing machines indeed capture the informal notion of effective method in logic ... Paul M.B. authorlink Paul Vitanyi title Turing machine year 2009 journal Scholarpedia volume 4 url http www.scholarpedia.org article Turing machine Importance of the Turing machine accessdate 23 April 2010 issn 1941 6016 quote In the last three quarter of a century the Turing machine model has proven ... more details
Infobox award name Turing Award image imagesize description Outstanding contributions in Computer science ... year 1966 year2 2010 website http awards.acm.org homepage.cfm?srt all&awd 140 ACM List of Turing Laureates The Turing Award , in full A.M. Turing Award , is an annual award given by the Association ... to the computer field . ref name ACM The Turing Award is recognized as the highest distinction in Computer ... room news releases 2007 turingaward title ACM S Turing Award Prize Raised To 250,000 publisher Association ... Geringer ref The award is named after Alan Turing Alan Mathison Turing , a British scientist, Mathematics .... Turing is frequently credited for being the Father of theory theoretical computer science and artificial ... ACM cite web title A. M. Turing Award publisher ACM url http awards.acm.org homepage.cfm?srt all&awd ... year history. ref name Allen cite press release title First Woman to Receive ACM Turing Award publisher ... Kolbasuk McGee title There s Still A Shortage Of Women In Tech, First Female Turing Award Winner Warns ... news author Perelman, Deborah title Turing Award Anoints First Female Recipient url http www.eweek.com ... for more detailed information on their achievements. Turing Award recipients class wikitable bgcolor ... to the theory of NP complete NP completeness 1986 flagicon USA John Hopcroft and br flagicon ..., widely adopted in the hardware and software industries. ref http www.ddj.com 206103622 2007 Turing ... computation, and the theory of parallel and distributed computing. See Also List of Turing Award laureates by university affiliation Notes reflist 2 External links commonscat Turing Award http awards.acm.org homepage.cfm?srt all&awd 140 ACM List of Turing Laureates http www.informatik.uni trier.de ley db journals cacm turing.html Bibliography of Turing Award lectures through 2000 Turing award Category Alan Turing Category Association for Computing Machinery Category Awards established in 1966 ... bg ca Premi Turing cs Turingova cena da Turing Award de Turing Award et Turingi ... more details
nofootnotes date February 2011 The Turing Baronetcy , of Foveran in the County of Aberdeen , is a title in the Baronetage of Nova Scotia . It was created in 1638 for John Turing. He was a supporter of Charles I of England Charles I and was taken prisoner by the Covenanter s in 1639. In 1651, he fought at the Battle of Worcester . The Turing family descends from Sir William Turing, a supporter of David II of Scotland David II , who was granted the barony of Foveran in Aberdeenshire by the king. The cryptographer and computing pioneer Alan Turing was the uncle of the twelfth Baronet. Turing Baronets, of Foveran 1638 Sir John Turing, 1st Baronet c. 1595 1662 Sir John Turing, 2nd Baronet d. 1682 Sir John Turing, 3rd Baronet 1680 1733 Sir Alexander Turing, 4th Baronet 1702 1782 Sir Inglis Turing, 5th Baronet 1743 1791 Sir Robert Turing, 6th Baronet 1745 1831 Sir James Henry Turing, 7th Baronet 1791 1860 Sir Robert Fraser Turing, 8th Baronet 1827 1913 Sir James Walter Turing, 9th Baronet 1862 1928 Sir Robert Andrew Henry Turing, 10th Baronet 1895 1970 Sir John Leslie Turing, 11th Baronet 1895 1987 Sir John Dermot Turing, 12th Baronet b. 1961 References Kidd, Charles, Williamson, David editors . Debrett s Peerage and Baronetage 1990 edition . New York St Martin s Press , 1990. rayment b . Category 1638 establishments in Nova Scotia Category Baronetcies Turing Category Alan Turing ... more details
Orphan date October 2008 The Turing Lecture is an annual event, co hosted by the British Computer Society BCS and Institution of Engineering and Technology IET , named in honour of the father of Computer Science , Alan Turing . The first Turing Lecture was hosted in 1998 , which was met with high levels of enthusiasm. Since the first Turing Lecture, which was a national event, a Manchester Turing Lecture has also been inaugurated. This event has been running since 2005 . Past speakers include industry heavyweights such as James Martin author James Martin , a noted Computing pioneer and Grady Booch , chief scientist for IBM. External links http www.bcs.org server.php?show nav.5826 BCS Turing Lecture home page http www.cs.manchester.ac.uk aboutus events Turing Manchester Turing Lecture home page Category Computer science education compsci stub ... more details
Turing is a stream cipher developed by Gregory G. Rose and Philip Hawkes at Qualcomm for CDMA . It is designed to be fast in software and achieves around 5.5 cycles byte on some x86 processors. Turing generates 160 bits of output in each round by applying a non linear filter to the internal state of an LFSR . See also SOBER 128 Helix cipher Helix External links http www.qualcomm.com.au news releases 2003 press1161.html Turing article at Qualcomm http www.jdudar.com turing index.html Java Implementation of Turing Algorithm References Gregory G. Rose and Philip Hawkes , Turing A Fast Stream Cipher, Fast Software Encryption 2003, pp290&ndash 306 http www.qualcomm.com.au PublicationsDocs Turing.pdf PDF . Antoine Joux and Fr d ric Muller, A Chosen IV Attack Against Turing, Selected Areas in Cryptography 2003, pp194&ndash 207. crypto stub Category Stream ciphers ... more details
Infobox book name The Annotated Turing A Guided Tour Through Alan Turing s Historic Paper on Computability and the Turing Machine image File The Annotated Turing cover.jpg 200px author Charles Petzold language English language English subject Mathematics and computing genre Non fiction publisher John Wiley & Sons pub date 2008 media type Print paperback pages 372 isbn 978 0470229057 oclc 2008022829 dewey 511.3 52 22 congress QA267 .P48 The Annotated Turing A Guided Tour Through Alan Turing s Historic Paper on Computability and the Turing Machine is a book by Charles Petzold , published in 2008 by John Wiley & Sons, Inc. Petzold annotates Alan Turing s paper On Computable Numbers, with an Application to the Entscheidungsproblem . The book takes readers sentence by sentence through Turing s paper providing explanations, further examples, corrections, and biographical information. Table of Contents Part I. Foundations Chapter 1 This Tomb Holds Diophantus Chapter 2 The Irrational and the Transcendental Chapter 3 Centuries of Progress Part II. Computable Numbers Chapter 4 The Education of Alan Turing Chapter 5 Machines at Work Chapter 6 Addition and Multiplication Chapter 7 Also Known as Subroutines Chapter 8 Everything is a Number Chapter 9 The Universal Machine Chapter 10 Computers and Computability Chapter 11 Of Machines and Men Part III. Das Entscheidungsproblem Chapter 12 Logic and Computability Chapter 13 Computable Functions Chapter 14 The Major Proof Chapter 15 The Lambda Calculus Chapter 16 Conceiving the Continuum Part IV. And Beyond Chapter 17 Is Everything a Turing Machine? Chapter 18 Diophantus Awakes External links http theannotatedturing.com The book s website http charlespetzold.com Charles Petzold s website http www.turing.org.uk Alan Turing website maintained by Andrew Hodges http www.alanturing.net The Turing Archive for the History of Computing http www.turingarchive.org The Turing Digital Archive DEFAULTSORT Annotated Turing Category 2008 books Category ... more details
Image Turingswitch.png right thumb 200px Turing switch The Turing switch is a logical construction similar to the Turing machine . The Turing switch models the operation of a basic network switch in a network of switches, much the same as a Turing machine models the operation of a basic computational entity. Both are named in honor of the English logician Alan Turing . Some introductory research on the Turing switch was started at the University of Cambridge by http www.cl.cam.ac.uk jac22 Jon Crowcroft . In essence, Crowcroft suggests that instead of using general purpose computers to do packet switching, the required operations should be reduced to application specific logic and then that application specific logic should be implemented using optical components. The work is not actually based on Turing s research. A Turing switch consists of a Switched fabric switching fabric , one or more ingress interfaces also referred to as sources , one or more egress interfaces sinks , and a decision procedure to determine an egress interface given an ingress interface. Interfaces are sometimes referred to as ports. A packet cell or switched unit arrives at an ingress interface, the appropriate egress interface is determined by the decision procedure, and the packet is then transported across the switching fabric to the egress interface. A packet is a symbol or sequence of 1 s and 0 s. An ingress interface is connected to an ingress line, an egress interface to an egress line. The ingress line is said to feed the ingress interface the egress interface feeds the egress line. ref Jon Crowcroft http www.cl.cam.ac.uk techreports UCAM CL TR 556.pdf Turing Switches. Turing machines for all optical Internet routing UCAM CL TR 556 ISSN 1476 2986 January 2003 ref See also Network switch References reflist Category Networks Category Telecommunications systems Category Routers Category Turing machine ... more details
Infobox Planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Turing symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered August 01, 1997 designations yes mp name 10204 alt names 1997 PK1 named after Alan Turing mp category orbit ref epoch May 14, 2008 aphelion 3.0313504 perihelion 2.5748530 semimajor eccentricity 0.0814272 period 1714.1811492 avg speed inclination 6.90329 asc node 143.24019 mean anomaly 359.00017 arg peri 295.25347 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 13.7 10204 Turing 1997 PK1 is a Asteroid belt main belt asteroid discovered on August 1, 1997 by P. G. Comba at Prescott Observatory Prescott . References references External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 10204 Turing JPL Small Body Database Browser on 10204 Turing MinorPlanets Navigator 10203 Flinders 10205 Pokorn MinorPlanets Footer DEFAULTSORT Turing Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Paul G. Comba Category Astronomical objects discovered in 1997 beltasteroid stub fa it 10204 Turing hu 10204 Turing pl 10204 Turing pt 10204 Turing ... more details
In computability theory , the Turing jump or Turing jump operator , named for Alan Turing , is an operation that assigns to each decision problem math X a successively harder decision problem math X &prime with the property that math X &prime is not decidable by an oracle machine with an oracle computer science oracle for math X . The operator is called a jump operator because it increases the Turing degree of the problem math X . That is, the problem math X &prime is not Turing reducible to math X . Post s theorem establishes a relationship between the Turing jump operator and the arithmetical hierarchy of sets of natural numbers. Informally, given a problems, the Turing jump returns gives the set of Turing machines which halt when given access to an oracle that solves that problem. Definition Given a set math X and a G del numbering math sub i sub sup X sup of the relative computability math X computable functions, the Turing jump math X &prime of math X is defined as math X x mid varphi x X x mbox is defined . math The math n th Turing jump math X sup n sup is defined inductively ... the math i th prime. The notation math 0&prime or math &prime is often used for the Turing jump of the empty ... 1987 . Examples The Turing jump math 0&prime of the empty set is Turing equivalent to the halting ... is math X computably enumerable but not math X computable function computable . If math A is Turing degree Turing equivalent to math B then math A &prime is Turing equivalent to math B &prime . The converse ... mapping math X to math X &prime is definable in the partial order of the Turing degrees. Many properties of the Turing jump operator are discussed in the article on Turing degree s. References ... of Turing Degrees last Hodes first Harold T. journal Journal of Symbolic Logic volume 45 year ... Defining the Turing jump journal Math. Res. Lett. volume 6 issue 5 6 pages 711 722 url http www.mrlonline.org ... Projekto matematiko Salto de Turing ja ... more details
other uses multiple issues citation style September 2010 cleanup September 2010 File Turing Test version 3.png thumb The standard interpretation of the Turing Test, in which player C, the interrogator ... adapted from Saygin, 2000. ref name Saygin 2000 Harvnb Saygin 2000 ref The Turing test is a proposal ... part of his Discourse on the Method and in 1950 precised by Alan Turing . A human judge ... only channel such as a keyboard computing computer keyboard and visual display unit screen . ref Turing ... in 1950. Harv Turing 1950 p 433 ref Alan Turing , in his 1950 paper Computing Machinery and Intelligence ... to define, Turing chooses to replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. ref name T433 Turing s new question is Are there imaginable digital computers which would do well in the imitation game? ref Harv Turing 1950 p 442 This particular version of the test was called The Imitation Game . Turing continues with a more ... satisfactorily the part of A in the imitation game, the part of B being taken by a man? Harv Turing 1950 p 442 ref This question, Turing believed, is one that can actually be answered. In the remainder ... below. Turing would probably reject convincingly as the kind of terminology that his test set out ... is very similar to the Turing test, but it is not certain that Ayer s popular philosophical classic was familiar to Turing. Alan Turing Researchers in the United Kingdom had been exploring machine ... and electronics researchers that included Alan Turing , after whom the test is named. ref Harvnb McCorduck 2004 p 95 ref Turing, in particular, had been tackling the notion of machine intelligence ... of computer intelligence was made by him in 1947. ref Harvnb Copeland 2003 p 2 ref In Turing s report ... to show intelligent behaviour ref Harvnb Turing 1948 p 412 ref and, as part of that investigation ... former undergraduate colleague, DG Champernowne , Turing began writing a chess program for a computer ... more details
, Turing s proof was the second proof of the assertion Alonzo Church proof was first ... ... Undecidable p. 145 . Turing preceded this proof with two others. The second and third both rely ... In 1905 Jules Richard presented this profound paradox. Alan Turing s first proof constructs this paradox ..., p. 61 . Complications Turing s proof is complicated by a large number of definitions, and confounded ... as given Davis s commentary in Undecidable, p. 115 . Turing himself published A correction in 1937 ... suggestions and Turing s corrections, errors remained in the description of the universal machine . And confusingly, since Turing was unable to correct his original paper, some text within the body harks to Turing s flawed first effort. Bernays corrections may be found in The Undecidable , pp. 152 ... version of Turing s paper has these corrections in an addendum however, corrections to the Universal ..., a machine is said to be circle free if it is a Turing computing ... machine which prints an infinite number of 0s and 1s. And the two theorems of Turing s in question are really the following. There is no Turing ... whether n is the D.N of a Turing computing ... machine that is circle free. Secondly , There is no Turing ... whether n is the D.N of a Turing computing ... machine that ever prints a given symbol 0 say Post ... The paper started attractively, but soon plunged in typical Turing manner into a thicket of obscure ..., Turing proceeded from two proofs that were to lead to his final proof. His first theorem is most ... ...we have no general process for doing this in a finite number of steps p. 132, ibid . Turing ... of M p. 148 Finally, in only 64 words and symbols Turing proves by reductio ad absurdum that the Hilbert Entscheidungsproblem can have no solution U p. 145 . Summary of the first proof Turing created ... Turing s machine H is attempting to print a diagonal number of 0s and 1s This diagonal number is created ... 1 or 0 of the R th successful machine Turing spent much of his paper actually constructing his machines ... more details
G del s completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence ... in every structure mathematical logic structure for its language. The completeness theorem shows ... logic. An important consequence of the completeness theorem is that it is possible to enumerate ... using axioms from the theory. G del s incompleteness theorem G del s in completeness theorem , referring to a different meaning of completeness , shows that if any sufficiently strong effective theory ... be proven nor disproven within the theory. Nevertheless the completeness theorem applies to these theories ..., the completeness theorem, it is necessary to also define a deductive system. A deductive ..., and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. Statement and consequences G del s completeness theorem says that a deductive system of first ... to prove all the logically valid formulas. A converse to completeness is soundness theorem soundness ... deduction. A more general version of G del s completeness theorem holds. It says that for any first ... called proof theory studies what can be formally proved in particular formal system s. The completeness ... semantics and syntax . The completeness theorem should not, however, be misinterpreted as obliterating ... theory Using the compactness and completeness theorems model theory Using the compactness and completeness theorems . In particular, G del s completeness theorem deals with formulas that are logical ... consequences of certain theories. An important consequence of the completeness theorem ... is not decidable set decidable . But the completeness theorem implies that the set of consequences ... theorem The completeness theorem and the compactness theorem are two cornerstones of first ... consequence of a finite subset of . This is an immediate consequence of the completeness ... more details
In mathematics , completeness is a fundamental property of the real number s that is a useful tool in calculus and real analysis . Intuitively, completeness states that there are not any gaps in Dedekind ... decimal number system , completeness is equivalent to the statement that any infinite ... of the real numbers used, completeness may take the form of an axiom the completeness ... forms of completeness, the most prominent being Dedekind completeness the least upper bound property and Cauchy completeness Complete metric space completeness as a metric space . Forms of completeness ... as an ordered field satisfying some version of the completeness axiom . Different versions of this axiom are all equivalent, in the sense that any ordered field that satisfies one form of completeness satisfies all of them. When the real numbers are instead constructed using a model, completeness becomes a theorem or collection of theorems. Dedekind completeness main Least upper bound property Dedekind completeness , also known as the least upper bound property , states that every nonempty ... approach to the real numbers, this is the version of completeness that is most often stated as an axiom ... upper bound y &isin Q with y x . Dedekind completeness is related to the construction ... to be the least upper bound of some set of rational numbers. In order theory , Dedekind completeness can be generalized to any partially ordered set . See completeness order theory . Cauchy completeness Cauchy completeness is the statement that every Cauchy sequence of real numbers convergent ... number line, this sequence converges to pi. Cauchy completeness is related to the construction ... of a Cauchy sequence of rational numbers. In mathematical analysis , Cauchy completeness can be generalized to a notion of completeness for any metric space . See complete metric space . Nested intervals theorem main Nested intervals The nested interval theorem is another form of completeness ... more details
In the mathematics mathematical area of order theory , completeness properties assert the existence of certain ... notions of completeness exist. The motivation for considering completeness properties derives from ... as total operations on a partially ordered set. For this reason, poset s with certain completeness ... the properties of the newly obtained operations yields further interesting subjects. Types of completeness properties All completeness properties are described along a similar scheme one describes .... Hence every completeness property has its duality order theory dual , obtained by inverting the order ... with the notion of bounded completeness given below. Finite completeness Further simple completeness conditions arise from the consideration of all non empty finite sets. An order in which ... . The dual notion is semilattice meet semilattice . Further completeness conditions The strongest form of completeness is the existence of all suprema and all infima. The posets with this property ... of possibly infinite subsets, that do not yield this strong completeness at once. If all directed set ... on suprema and there is no common name for the dual property. However, bounded completeness can be expressed in terms of other completeness conditions that are easily dualized see below . Although ... between completeness properties It was already observed that binary meets joins yield all ... the existence of all suprema. Bounded completeness can also be characterized differently. By an argument ... of the set of upper bounds. Consequently, bounded completeness is equivalent to the existence of all ... of this set which exists by directed completeness is equal to the supremum of X . Thus every ..., and to make directed completeness equivalent to completeness, it is convenient to assume also that there are only ... to the basis completion of x D x is isolated in D . Traditional notions of completeness a can be found ... , the underlying domain is incomplete in Actor model Actor semantics . Completeness in terms ... more details
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