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	Entscheidungsproblem - Wikipedia, the free encyclopedia
		The Entscheidungsproblem (English: decision problem) is the challenge in symbolic logic to find a general algorithm which decides for given first-order statements whether they are universally valid or not.
		Turing reduced the halting problem for Turing machines to the Entscheidungsproblem, and his paper is generally considered to be much more influential than Church's.
		The Entscheidungsproblem is related to Hilbert's tenth problem, which asks for an algorithm to decide whether or not Diophantine equations have a solution.
	en.wikipedia.org /wiki/Entscheidungsproblem (644 words)

	Entscheidungsproblem - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-18)
		The work of both authors was heavily influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers to logical formulas in order to reduce logic to arithmetic.
		Die Wahl der Rechtsform als Entscheidungsproblem: Unter besonderer Berücksichtigung einer mittelständischen Unternehmung (Betriebspolitische Schriften ; Bd.
		Eigen- und/oder Fremdforschung und -entwicklung als strategisches Entscheidungsproblem
	encyclopedia.worldsearch.com /entscheidungsproblem.htm (668 words)

	Entscheidungsproblem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		Church proved that there is no algorithm (defined via (Click link for more info and facts about recursive function) recursive functions) which decides for two given lambda calculus expressions whether they are equivalent or not.
		Turing reduced the (Click link for more info and facts about halting problem) halting problem for Turing machines to the Entscheidungsproblem, and his paper is generally considered to be much more influential than Church's.
		The work of both authors was heavily influenced by (Click link for more info and facts about Kurt Gödel) Kurt Gödel's earlier work on his (Click link for more info and facts about incompleteness theorem) incompleteness theorem, especially by the method of assigning numbers to logical formulas in order to reduce logic to arithmetic.
	www.absoluteastronomy.com /encyclopedia/E/En/Entscheidungsproblem.htm (648 words)

	Entscheidungsproblem: Definition and Links by Encyclopedian.com - All about Entscheidungsproblem
		Alonzo Church and independently Alan Turing showed in 1936 that this is impossible.
		The negative answer to the Entscheidungsproblem was then given by Alonzo Church in 1936 and independently shortly thereafter by Alan Turing, also in 1936.
		Alan Turing, "On computable numbers, with an application to the Entscheidungsproblem", Proceedings of the London Mathematical Society, Series 2, 42 (1936), pp 230-265.
	www.encyclopedian.com /en/Entscheidungsproblem.html (590 words)

	Alan Turing: Tutte le informazioni su Alan Turing su Encyclopedia.it
		Nel 1934 si laureò con il massimo dei voti, l'anno seguente ottenne una fellowship e nel 1936 vinse il premio Smith.
		Proprio nel 1936 si trasferì alla Princeton University per conseguire il Ph.D., e pubblicò l'articolo "On computable Number, with an application to the Entscheidungsproblem" dove descriveva quella che verrà poi definita come la macchina di Turing e che lo consegnerà alla storia.
		La madre sostenne che il figlio, con le dita sporche per qualche esperimento chimico, avesse ingerito per errore la dose fatale di veleno; ma il verdetto ufficiale parlò senza incertezze di suicidio.
	www.encyclopedia.it /a/al/alan_turing.html (694 words)

	LEO Archive: entscheidungsproblem - Entscheidungsproblem (Site not responding. Last check: 2007-10-18)
		In 1936 an English mathematician, Alan Mathison Turing, in a paper published in the Proceedings of the London Mathematical Society (''On Computable Numbers with an Application to the Entscheidungsproblem''), conceived a logical machine the output of which could be used to define a computable number.
		This appears to be a linguistic form of the Entscheidungsproblem, which has attracted so much attention in the field of symbolic logic.
		Namely, it would obviously mean that in spite of the undecidability of the Entscheidungsproblem, the mental work of a mathematician concerning Yes-or-No questions could be completely2 replaced by a machine.
	forum.leo.org /archiv/2004_01/18/20040118014510w_en.html (222 words)

	Encyclopedia: Entscheidungsproblem
		In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers.
		The non-existence of such an algorithm (proven by Matiyasevich in 1970) implies a negative answer to the Entscheidungsproblem.
		Matiyasevichs theorem, proven in 1970 by Yuri Matiyasevich, implies that Hilberts tenth problem is unsolvable.
	www.nationmaster.com /encyclopedia/Entscheidungsproblem (1579 words)

	Entscheidungsproblem - Wikipedia
		El Entscheidungsproblem (en castellano: problema de decisión) es el reto en lógica simbólica de encontrar un algoritmo general que decida si una fórmula del cálculo de primer orden es un teorema.
		En el sentido que se pueden resolver exactamente los mismos problemas con ambos enfoques.
		La respuesta negativa al Entscheidungsproblem fue dada por Alonzo Church en 1936 e independientemente, muy poco tiempo después por Alan Turing, también en 1936.
	es.wikipedia.org /wiki/Entscheidungsproblem (647 words)

	decision processes: Metalogic B - abelard
		It could even be said that elephants, atoms and lesser particles make constant decisions as they bustle about their business.
		While I much prefer Turing’s engineering approach to the Entscheidungsproblem to that of Gödel, it is my judgement that Turing’s approach still remains insufficiently empiric.
		Entscheidungsproblem - decision problem, often referred to as the halting problem.
	www.abelard.org /metalogic/metalogicB1.htm (6186 words)

	Year 2 Communication Skills Essay: Alan Turing (Site not responding. Last check: 2007-10-18)
		One of Turing's schedule B courses was in Foundations of Mathematics taken by M. Newman, who asked if there was there "a mechanical process" which could show whether a statement was provable [8].
		This applied to the Entscheidungsproblem because it showed that the rational numbers gave rise to irrational numbers, and hence computable numbers gave rise to uncomputable numbers, and an uncomputable number is an example of an unsolvable problem.
		In 1938 the Government planned to take on 60 extra cryptanalysts in the event of war [14] and Alan Turing was one of these.
	www.selsyn.co.uk /pkent/p/essay2.html (2346 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		He was accepted by Cambridge in 1930 to study mathematics, and became a Fellow of Kings College in 1934 at the age of 22, completing a dissertation that extended group theory models of Von Neumann.
		Gödel showed that the Entscheidungsproblem (“decision problem”) was in principle unsolvable by logic, and this led to work by many mathematicians to further explain the theory and philosophy of mathematical unsolvability in terms of logic or other models of mathematics.
		By contrast, Turing showed by computers that the Entscheidungsproblem could not be solved, because the “halting problem” of Turing machines was itself unsolvable.
	grace.evergreen.edu /artofcomp/Articles/BeyondTuringMachines.html (1545 words)

	Entscheidungsproblem (Site not responding. Last check: 2007-10-18)
		El Entscheidungsproblem (Alemán: el problema de la decisión) es el desafío en la lógica simbólica para encontrar un algoritmo general que decida para las declaraciones de primer orden dadas a si él es universal válido o no. La iglesia de Alonzo y Alan Turing mostró independientemente en 1936 que esto es imposible.
		La respuesta negativa al Entscheidungsproblem entonces fue dada por Alonzo Church en 1936 e independientemente pronto después de eso por Alan Turing, también en 1936.
		Turing redujo el Entscheidungsproblem al problema que paraba para las máquinas de Turing, y su papel se considera generalmente ser mucho más influyente que la iglesia.
	www.yotor.net /wiki/es/en/Entscheidungsproblem.htm (641 words)

	On computable numbers, with an application to the Entscheidungsproblem - A. M. Turing, 1936 (Site not responding. Last check: 2007-10-18)
		The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means.
		In particular, it is shown (§11) that the Hilbertian Entscheidungsproblem can have no solution.
		In a recent paper Alonzo Church[2] has introduced an idea of "effective calculability", which is equivalent to my "computability", but is very differently defined.
	www.cs.wpi.edu /~dd/courses/503/03-fall/turing.html (7410 words)

	Entscheidungsproblem - netlexikon
		Als Entscheidungsproblem bezeichnet man heute in der Theoretischen Informatik allgemein Probleme, für die zu einer gegebenen Eingabe als Lösung nur zwei Antworten (z.
		Ursprünglich galt als Entscheidungsproblem die Frage, ob es einen Algorithmus gibt, der für einen beliebigen Ausdruck in der Prädikatenlogik bestimmt, ob es sich um eine Tautologie handelt oder nicht.
		Dieses (spezielle) Entscheidungsproblem wurde 1928 von David Hilbert gestellt (siehe Hilbertprogramm) und 1930 von Kurt Gödel negativ beantwortet (siehe Gödelscher Unvollständigkeitssatz).
	www.lexikon-definition.de /Entscheidungsproblem.html (298 words)

	Ambiguous Turing.
		His war-time code-breaking may be the most famous; but perhaps the most important was the idea of the Turing machine, the theoretical apparatus which defined computation and computers.
		The Entscheidungsproblem, posed by Hilbert, asks whether there is any mechanical procedure for determining whether a mathematical problem is solvable.
		The clear conception of computation which the Turing machine provided allowed Turing to show that the Entscheidungsproblem had to be answered in the negative — there is no general procedure which can deal with all mathematical problems, even in principle.
	www.consciousentities.com /turing.htm (807 words)

	[No title]
		Entscheidungsproblem" Alan Turing tried to capture this notion formally with the introduction of Turing machines.
		In that paper he showed that the 'Entscheidungsproblem' could not be solved.
		Turing, A.M. On Computable Numbers, with an Application to the Entscheidungsproblem (http://www.abelard.org/turpap2/tp2-ie.asp)", Proceedings of the London Mathematical Society, Series 2, 42 (1936-37), pp.230-265.
	en-cyclopedia.com /wiki/Church-Turing_thesis (1055 words)

	Citations: On Computable Numbers, with an Application to the Entscheidungsproblem - Turing (ResearchIndex)
		Turing, A. On computable numbers, with an application to the entscheidungsproblem', Proceedings of the London Mathematical Society 42, 230--265.
		Turing himself never claimed that TMs formalize all of computation, and in fact made claims that suggested the opposite [WG02] 3.2 Incompleteness of interactive systems Godel showed that arithmetic over the integers cannot be completely formalized by logic, because not all its properties are....
		Turing, A., On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society 42 (1936), 230--265, correction in Proceedings of the London Mathematical Society 43 (1937), 544-- 546.
	citeseer.ist.psu.edu /context/13532/0 (889 words)

	Citations: with an application to the entscheidungsproblem - TURING (ResearchIndex)
		He also uses Cantor s method to diagonalize over the countable set of computable real numbers and construct an uncomputable real, from which he deduces the unsolvability of the halting....
		The Entscheidungsproblem asks whether there exists a definite method or algorithm which (at least in principle) can be applied to any given mathematical property to....
		For instance, when a human agent computes internally what he should write as message, the observation of this process is the written message (interaction object) that is....
	citeseer.ist.psu.edu /context/73686/0 (1760 words)

	CSC 110 Topic 30
		The entscheidungsproblem (decision problem in English) refers to the problem, posed by German mathematician David Hilbert, of whether an algorithm exists that can determine whether a given arithmetic statement is true or not (the word true here means that the statement could be proven true within a given mathematical/logical framework).
		Assuming the correctness of the Church-Turing thesis discussed in topic 29, an algorithm satisfying the requirements of Hilbert's decision problem is equivalent to a Turing machine which, when provided with any arithmetic statement on its tape, would eventually produce the answer yes if the statement is true or no if it is not.
		The halting problem, like David Hilbert's entscheidungsproblem, is an example of a class of problems known as decision problems.
	www.augustana.ab.ca /~hackw/csc110/topic/top30.html (1166 words)

	Entscheidungsproblem Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-18)
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	www.karr.net /encyclopedia/Entscheidungsproblem (783 words)

	Rober Rosen - Effective Processes, Computation and Complexity
		Indeed, sometimes it is just as important and profound to prove that a given problem, or class of problems, is unsolvable.
		However, in order to solve the Entscheidungsproblem in any kind of definitive fashion, it was necessary to create a formal notion of "procedure", which could then be used in a proof to provide either a positive solution (i.e., show that an algorithm does exist) or a negative solution (i.e., show that no possible algorithm exists).
		Not surprisingly, then, both Church and Turing came to the same conclusion regarding the Entscheidungsproblem: it was unsolvable.
	www.panmere.com /rosen/effprocess1.htm (3198 words)

	56 - Cryptonomicon - Entscheidungsproblem (Site not responding. Last check: 2007-10-18)
		The British mathematician Alan Turing however seized upon the idea of a machine as a solution to the problem.
		He presented his work in 1936 in his paper 'On Computable Numbers with an Application to the Entscheidungsproblem'.
		This was where the concept of a Turing Machine first appeared and was actually an answer to an altered form of the Entscheidungsproblem.
	www.electricinca.com /56/annotations/entscheidungsproblem.htm (215 words)

	The New York Review of Books: 'A MATTER OF TEMPERAMENT'
		He dreamed of solving the Entscheidungsproblem and thereby solving as corollaries all the famous unsolved problems of mathematics....
		This was the tone of his general lecture course on the philosophy of science which I heard him give in late 1931.
		In 1931, just as Hilbert asserted that we must know, Kurt Gödel showed that the Entscheidungsproblem in fact could not be solved—more explicitly that it could not be solved in the formal system of Whitehead and Russell's "Principia Mathematica" and the methods derived in that system.
	www.nybooks.com /articles/1780 (1029 words)

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