In computability theory computer science computability theory , the haltingproblem is a decision problem ..., or will run forever. Alan Turing proved in 1936 that a general algorithm to solve the haltingproblem for all possible program input pairs cannot exist. We say that the haltingproblem is Undecidable problem undecidable over Turing machine s. B. Jack Copeland 2004 attributes the actual term halting ... Hodges does not have the word halting or words haltingproblem in his index. The earliest known use of the words haltingproblem is in a proof by Davis p. 70&ndash 71, Davis 1958 Theorem 2.2 There exists a Turing machine whose haltingproblem is recursively unsolvable . A related problem is the printing ... that The haltingproblem was so named and it appears, first stated by Martin Davis cf Copeland footnote ... , but strictly this is not true . p. 40 For more see the History of the haltingproblem History section above. ref Formal statement The haltingproblem is a decision problem about properties of computer ... and input to decide whether the program stops when run with that input. Representing the haltingproblem ... x represents the haltingproblem. This set is recursively enumerable , which means there is a computable ... is not recursively enumerable. There are many equivalent formulations of the haltingproblem any set whose Turing degree equals that of the haltingproblem is such a formulation. Examples of such sets ... of the haltingproblem s undecidability is that there cannot be a general algorithm that decides ... program halts, which is impossible, since the haltingproblem is undecidable. Yet another consequence of the undecidability of the haltingproblem is Rice s theorem which states that the truth ... degree as the haltingproblem. It is a normal number normal and transcendental number which can ... . Since the negative answer to the haltingproblem shows that there are problems that cannot be solved ... in the form of a calculating machine a hypercomputer that could solve the haltingproblem for a Turing ... more details
Summary wvbailey User Wvbailey Wvbailey 19 51, 29 June 2006 UTC drawn in Autosketch by wvbailey, 2006 06 29 following proof and illustrations on p. 148 149, Marvin Minsky, Computation Finite and Infinite Machines, Pentice Hall, Englewood Cliffs, N.J. 1967. Licensing GFDL self with disclaimers migration relicense ... more details
Summary wvbailey User Wvbailey Wvbailey 16 08, 30 June 2006 UTC , after Minsky 1967. Drawn with Autosketch 2006 06 30 Licensing GFDL self with disclaimers migration relicense ... more details
A halting site is a facility constructed for the accommodation of Irish travellers itinerants and other nomadic groups. They are common in Ireland , mainly on the periphery of towns, where they are maintained by local authorities , and include spaces to park travel trailer caravan s and vehicles, electricity and sanitary services, and space to graze horses. Halting sites are often controversial due to opposition from local residents ref cite web url http www.iol.ie fcrg title Foxborough Concerned Residents Group publisher Foxborough Concerned Residents Group Lucan, Co. Dublin accessdate 2009 05 06 ref , and anti social activity such as inter clan violence, illegal dumping, and general crime. ref cite web url http www.rte.ie news 2004 1019 travellers.html title Six arrested after halting site raids publisher RT accessdate 2009 05 06 ref ref cite web url http www.irishtimes.com newspaper breaking 2009 0403 breaking60.htm title Garda seize weapons after feud on Dublin halting site publisher Irish Times accessdate 2009 05 06 ref ref cite web url http www.irishnews.com break.asp?tbrk brk&par brk&catid 5834&subcatid 642&storyid 409077 title Man held after halting site drugs seizure publisher Irish News accessdate 2009 05 06 ref The term halting site can also refer to unofficial encampments established by large groups of travellers on waste land or illegally seized private land, who sometimes demand large amounts of compensation to leave. ref cite web url http www.independent.ie national news travellers demand 6m housing on fingal council site 124596.html title Travellers demand 6m housing on Fingal Council site publisher Irish Independent accessdate 2009 05 06 ref ref cite web url http www.independent.ie national news travellers on illegal dump want compensation for building work 484935.html title Travellers on illegal dump want compensation for building work publisher Irish ... 06 ref See also Dale Farm a prominent halting site in England. References refs Category Irish Travellers ... more details
Infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name Halting State image image Halting State 1stEd .jpg 200px image caption Cover of first edition hardcover author Charles Stross cover artist country United Kingdom UK & United States US language English language English genre Science fiction publisher Orbit Books Orbit UK , Ace Books Ace US release date October 2, 2007 media type Print Hardcover pages 368 pp isbn 0 441 01498 4 dewey 823 .92 22 congress PR6119.T79 H36 2007 oclc 123232449 Halting State is a novel by Charles Stross , published in the United States on October 2, 2007 and in the UK in January, 2008. ref http www.antipope.org charlie blog static 2007 10 ahem.html Charlie s Diary Ahem Bot generated title ref Stross has said that it is a Thriller genre thriller set in the software houses that write MMORPG multiplayer games . ref http sfrevu.com php Review id.php?id 5071 SFRevu Review Bot generated title ref The plot centres around a bank robbery in a virtual world. ref http www.boingboing.net 2007 10 02 charlie strosss halt.html Charlie Stross s Halting State Heist novel about an MMORPG Boing Boing Bot generated title ref It features speculative technologies, including Specs and virtual server networks over mobile phones. The book is on its second printing in the United States. ref name Charles Stross 2007 10 12 http video.google.com videoplay?docid 1670032014558458068&hl en Charles Stross 2007 10 12 Bot generated title ref The novel was nominated for both the Hugo Award Hugo and Locus Awards in 2008. ref name WWE 2008 cite web url http ... fake faux email to supporting characters. A sequel to Halting State entitled Rule 34 previously 419 ... Halting State was nominated for the both the Hugo and Locus Awards in 2008, ref name WWE 2008 and The Guardian ... links http www.worldswithoutend.com novel.asp?ID 1039 Halting State at Worlds Without End http www.sfbrp.com archives 61 Audio review and discussion of Halting State at http www.sfbrp.com The Science ... more details
No Problem may refer to No Problem Sonny Rollins album No Problem Sonny Rollins album , a 1981 album No Problem Fann Wong album No Problem Fann Wong album , a 2000 album No Problem TV series No Problem TV series , a British television series No Problem film No Problem film , a 2010 Bollywood film disambig ... more details
Otheruses Wiktionary A problem is an obstacle, impediment, difficulty or challenge, or any situation ... purpose or goal. Individual awareness of a problem constitutes awareness of a desired outcome ... the outcome from taking place. Problem solving main Problem solving Every theoretical problem asks for an answer or solution. Trying to find a solution to a problem is known as problem solving . That is, a problem is a gap between an actual and desired situation. The time it takes to solve a problem ... classified as an open problem . See also List of unsolved problems From the mid 20th century, the field ... Mathematical problem is a question about mathematical objects and structures that may require a distinct answer or explanation or mathematical proof proof . Examples include Word problem mathematics ... with only four colours . In society , a problem can refer to particular social issue s, which if solved ... hostility and disruption. See also Wicked problem In business and engineering , a problem is a difference between actual conditions and those that are required or desired. Often, the causes of a problem ... corrective actions. In Chess problem chess , a problem is a puzzle set by somebody using chess pieces .... In theology , there is what is referred to as the Synoptic Problem , which includes in its ... in the Gospels accounts of allegedly historical events. In academic discourse a problem is a challenge ... or idea. An optimization problem is finding the best solution from all feasible solutions. A good example of this type of problem is the travelling salesperson problem which is based on calculating the most efficient route between many places In computability theory a decision problem requires a simple yes or no answer. In rock climbing a problem is a series of Rock geology rock s that forces the climber to climb. In Reading process reading , a problem is a combination of a series of words ... problem is presented. Motion physics Motion is achieved via mechanical interaction of the legs and a surface ... more details
Summary Low res scan of book cover Halting State by Charles Stross, 2007 Ace Books first edition hardcover for use in illustrating article about book. Retrieved from http sitb images.amazon.com Qffs v35ler3cmP6d6 ynRdlAhPLLFgxLszL5rWUzWIahntGDJERBPqDFcbWVzhW. Licensing Non free book cover Non free media rationale Article Halting State Description Book Cover Source Derived from a digital capture photo scan of the book cover creator of this digital version is irrelevant as the copyright in all equivalent images is still held by the same party . Copyright held by the publisher or the artist. Claimed as fair use regardless. Portion Book cover only, a small portion of the commercial product. Low resolution Yes Purpose The image serves as the primary means of visual identification of the subject the book . It illustrates educational articles about the book from which the cover illustration was taken. Replaceability There is no free equivalent of this book cover, so the image cannot be replaced by a free image. other information The use of the cover will not affect the value of the original work or limit the copyright holder s rights or ability to distribute the original. In particular, copies could not be used to make illegal copies of the book. category Book covers Halting State ... more details
quintic equation algebraically. Also provably unsolvable are so called undecidable problem s, such as the haltingproblem for Turing machine s. Many abstract problems can be solved routinely, others ...A mathematical problem is a problem that is amenable to being analyzed, and possibly solved, with the methods of mathematics . This can be a real world problem, such as computing the Orbit Planetary orbits orbit s of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert s problems . It can also be a problem referring to the Foundations of mathematics nature of mathematics itself, such as Russell s Paradox . Real world problems Informal real world mathematical problems are questions related to a concrete setting, such as Adam has five apples and gives John three. How many has he left? . Such questions are usually more difficult to solve than regular mathematical exercises like 5 &minus 3 , even if one knows the mathematics required to solve the problem. Known as word problem mathematics education word problem s, they are used in mathematics education to teach students to connect real world situations to the abstract language of mathematics. In general, to use mathematics for solving a real world problem, the first step is to construct a mathematical model of the problem. This involves abstraction from the details of the problem, and the modeller has to be careful not to lose essential aspects in translating the original problem into a mathematical one. After the problem has been solved in the world of mathematics, the solution must be translated back into the context of the original problem. Abstract problems Abstract mathematical problems arise in all fields of mathematics. While mathematicians usually study them for their own sake, by doing so results may be obtained that find application outside the realm of mathematics. Theoretical ... also List of unsolved problems in mathematics Problem solving Mathematical game External links http ... more details
problem in computability theory In computability theory computer science computability theory , the haltingproblem is a decision problem which can be stated as follows Given a description of a computer .... Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the haltingproblem for all possible program input pairs necessarily cannot exist. Hence, the haltingproblem is undecidability undecidable for Turing machines. Relationship with G del s incompleteness theorem The concept s raised by G del s incompleteness theorem s are very similar to those raised by the haltingproblem, and the proofs are quite similar. In fact, a weaker form of the First Incompleteness Theorem is an easy consequence of the undecidability of the haltingproblem. This weaker form ... form of the theorem can be proved from the undecidability of the haltingproblem as follows ... to decide the haltingproblem. Since we know that there cannot be such an algorithm, it follows ... that the haltingproblem the question of whether or not a Turing machine halts on a given program ... problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes or no answer. A decision problem is any arbitrary yes or no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns yes . These inputs can be natural numbers .... Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set ... numbers. Formally, a decision problem is a subset of the natural numbers. The corresponding informal problem is that of deciding whether a given number is in the set. A decision problem A is called decidable or effectively solvable if A is a recursive set . A problem is called partially ... not to statements but to decision problem s, which are countably infinite sets of questions each ... more details
. The haltingproblem is an important undecidable decision problem for more examples, see list ...Image Decision Problem.png thumb 200px A decision problem has only two possible outputs, yes or no or alternately ... problem is a question in some formal system with a yes or no answer, depending on the values of some input parameters. For example, the problem given two numbers x and y , does x evenly divide y ? is a decision problem. The answer can be either yes or no , and depends upon the values of x and y ... complex than a simple yes or no . A corresponding function problem is given two numbers x and y , what is x divided by y ? . They are also related to optimization problem s, which are concerned with finding the best answer to a particular problem. A method for solving a decision problem given in the form of an algorithm is called a decision procedure for that problem. A decision procedure for the decision problem given two numbers x and y , does x evenly divide y ? would give the steps for determining ... problem which can be solved by an algorithm, such as this example, is called decidable . The field ... by the most efficient algorithm for a certain problem. The field of recursion theory , meanwhile, categorizes .... As explained in the section decision problem Equivalence with function problems Equivalence with function problems below, there is no loss of generality. Definition A decision problem is any arbitrary ... the decision problem equivalently as the set of inputs for which the problem returns yes . These inputs ... be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language ... in terms of subsets of the natural numbers. Formally, a decision problem is a subset of the natural numbers. The corresponding informal problem is that of deciding whether a given number is in the set. Examples A classic example of a decidable decision problem is the set of prime numbers. It is possible ... of any effective method is enough to establish decidability. Decidability main Undecidable problem ... more details
The term word problem has several meanings word problem mathematics education is a type of textbook problem designed to help students apply abstract mathematical concepts to real world situations word problem mathematics is the word problem for encodings of sets in mathematics and computer science word problem for groups is the problem of recognizing the identity element in a finitely presented group word problem computability is a decision problem concerning formal languages mathdab ... more details
Alfred Tarski asked the following mathematical questions For Tarski s problem about the elementary theory of free groups see free group . Tarski s circle squaring problem Tarski s plank problem Tarski s exponential function problem Tarski monster group Tarski s high school algebra problem mathdab ... more details
Wiktionary problem A problem is an obstacle which hinders the achievement of a particular goal, objective or purpose. Problem s or The Problem may also refer to Problems Aristotle Problems Aristotle , an Aristotelian or pseudo Aristotelian collection of problems in question and answer form The Problem play The Problem play , a play by A. R. Gurney In music The Problem album The Problem album , an album by Mathematics Problem arlo Akrobata song Problem arlo Akrobata song Problem , a song by Remy Zero from Villa Elaine Problems , a song by Against Me from Searching for a Former Clarity Problems , a song by AZ from 9 Lives AZ album 9 Lives Problems , a song by Ben Kweller from Freak Out, It s Ben Kweller Problems , a song by Bran Van 3000 from Glee Bran Van 3000 album Glee Problems , a song by The Everly Brothers Problems , a song by Sex Pistols from Never Mind the Bollocks, Here s the Sex Pistols See also Mathematical problem Chess problem Lookfrom Problem Intitle Problem disambig sl Problem razlo itev ... more details
In scientific disciplines, a toy problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. For instance, while engineering a large system, the large problem is often broken down into many smaller toy problems which have been understood in good detail. Often these problems distill a few important aspects of complicated problems so that they can be studied in isolation. Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems. See, for example Santa Fe Ant Trail problem Secretary problem Missionaries and cannibals problem Monkey and Banana problem N Queens problem Firing squad synchronization problem Category Mathematics education Category Information science math stub eo Luda problemo ... more details
Counting problem may refer to Enumeration Combinatorial enumeration Counting problem complexity disambig Long comment to avoid being listed on short pages ... more details
Wiktionary Problem Child may refer to In film and television Problem Child film Problem Child film , a 1990 American comedy, followed by two sequels Problem Child TV series Problem Child TV series , an animated series based on the films Problem Child , an List of Instant Star episodes Season 2 2006 Instant Star episode Problem Child , an List of Umineko no Naku Koro ni episodes ep22 Umineko no Naku Koro ni episode In music Problem Child The Damned song Problem Child The Damned song Problem Child , a The Beach Boys discography song by the Beach Boys Problem Child , a song by AC DC from Dirty Deeds Done Dirt Cheap Problem Child , a song by Glue Gun from The Scene Is Not for Sale Problem Child , a song by Roy Orbison from Roy Orbison at the Rock House Problem Child, a 1980s band featuring Louis Prima Jr In other uses Problem Child , a boat that set a List of vehicle speed records Watercraft speed record disambig ... more details
Unreferenced auto yes date December 2009 Problem finding means problem discovery. It is part of the larger problem process that includes problem shaping and problem solving . Problem finding requires intellectual vision and insight into what is missing. This involves the application of creativity . Finding a problem can, depending on the problem, be either much easier or much harder than solving the problem. An example of a problem that was much easier to find than to solve is Fermat s Last Theorem . The problem is simple, is it true that it is impossible to separate any power higher than the second into two like powers? Solving the problem took 357 years. 1.1 CPF creative problem finding and CSPF creative science problem finding were put forward by professor Hu Weiping,China. See also Portal Thinking div style moz column count 3 column count 3 Abductive reasoning Analogy Artificial intelligence Brainstorming Common sense Common sense reasoning Creative problem solving Cyc Deductive reasoning Divergent thinking Educational psychology Executive function Facilitation General Problem Solver General problem solver Inductive reasoning Innovation Intelligence amplification Inquiry Morphological Analysis Allen Newell Newell, Allen PDCA Portal thinking Problem Statement Herbert Simon Simon, Herbert Soar cognitive architecture Thought Transdisciplinary Studies TRIZ Troubleshooting Wicked problem div DEFAULTSORT Problem Finding Category Problem solving Sci stub it Problem solving ... more details
Notability date May 2009 A problem statement is a concise description of the issues that need to be addressed by a problem solving team and should be presented to them or created by them before they try to solve the problem. When bringing together a team to achieve a particular purpose provide them with a problem statement . A good problem statement should answer these questions What is the problem? This should explain why the team is needed. Who has the problem or who is the client customer? This should explain who needs the solution and who will decide the problem has been solved. What form can the resolution be? What is the scope and limitations in time, money, resources, technologies that can be used to solve the problem? Does the client want a white paper ? A web tool? A new feature for a product? A brainstorming on a topic? The primary purpose of a problem statement is to focus the attention of the problem solving team. However, if the focus of the problem is too narrow or the scope of the solution too limited the creativity and innovation of the solution can be stifling. In project management, the problem statement is part of the project charter. It lists what s essential about ... March 22, 2010 ref A research worthy problem statement is the description of an active challenge i.e. problem faced by researchers and or practitioners that does not have adequate solutions available ... foundation. The research worthy problem statement should address all six questions what, how, where, when, why, and who. On the other hand, a statement of the problem is one or two sentences claim that outlines the problem that the study addresses. The statement of the problem should briefly address the question What is the problem that the research will address? ref Ellis, T. J., & Levy, Y. in press . A framework of problem based research A guide for novice researchers. Informing Science Journal . ref References Reflist Category Problem solving ru ... more details
Unreferenced stub auto yes date December 2009 Problem shaping means revising a question so that the solution process can begin or continue. It is part of the larger problem process that includes problem finding and problem solving . Problem shaping or problem framing often involves the application of critical thinking . Algorithm ic approach to technical problems reformulation was introduced by G. S. Altshuller in ARIZ . See also div style moz column count 3 column count 3 Adaptive Reasoning Abductive reasoning Analogy Artificial intelligence Brainstorming Common sense Common sense reasoning Creative problem solving Cyc Deductive reasoning Divergent thinking Educational psychology Executive function Facilitation General Problem Solver General problem solver Inductive reasoning Innovation Intelligence amplification Inquiry Morphological Analysis Allen Newell Newell, Allen PDCA Portal thinking Problem Statement Herbert Simon Simon, Herbert Soar cognitive architecture Thought Transdisciplinary Studies TRIZ Troubleshooting Wicked problem div DEFAULTSORT Problem Shaping Category Problem solving Sci stub it Problem shaping ... more details
Isomorphism problem may refer to graph isomorphism problem group isomorphism problem mathdab Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
unsourced date October 2010 The 1 center problem or minimax or minmax location problem is a classical combinatorial optimization problem in operations research of facilities location type. In its most general case the problem is stated as follows given a set of n demand points, a space of feasible locations of a facility and a function to calculate the transportation cost between a facility and any demand point, find a location of the facility which minimizes the maximum facility demand point transportation cost. The simple special case when the feasible locations and demand points are in the plane with Euclidean distance as transportation cost planar minmax Euclidean facility location problem, Euclidean 1 center problem in the plane, etc. , it is also known as the smallest circle problem . Its generalization to n dimensional Euclidean spaces is known as the smallest enclosing ball problem. A further generalization weighted Euclidean facility location is when the set of weights is assigned to demand points and the transportation cost is the sum of the products of distances by the corresponding weights. There are numerous particular cases of the problem, depending on the choice of the locations both of demand points and facilities, as well as the distance function. See also Minsum facility location 1 median problem , with geometric median being a special case Maxmin facility location obnoxious facility location k center problem k median problem Category Combinatorial optimization Category Operations research ... more details
In mathematics, Motz s problem is a problem which is widely employed as a benchmark for Mathematical singularity singularity problems to compare the effectiveness of numerical methods . The problem was first presented in 1947 by H. Motz in the paper The treatment of singularities of partial differential equations by relaxation methods . Category Partial differential equations Category Finite element method Mathanalysis stub ... more details
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