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...n 1953,<ref>{{cite journal| last1=Turing| first1=A. M. | author1-link=Alan Turing | title=Some Calculations of the Riemann Zeta-Function | doi=10.1112/plms/s [[Category:Alan Turing]] ...

...enumerability relative to [[oracle machine|oracles]]. It is named after [[Alan Selman]], who proved it as part of his PhD thesis in 1971. Informally, a set ''A'' is enumeration-reducible to a set ''B'' if there is a Turing machine which receives an enumeration of ''B'' (it has a special instructio ...

...on of the class NP that does not invoke a model of computation such as a [[Turing machine]]. The theorem was proven by [[Ronald Fagin]] in 1974 (strictly, i ...1=Neil D. | last2=Selman | first2=Alan L.|author2-link=Alan Selman | title=Turing machines and the spectra of first-order formulas | zbl=0288.02021 | journal ...

...lector. Hasenjaeger could take some comfort from the fact that even [[Alan Turing]] missed this weakness. Instead, the honour was attributed to [[Gordon Welc ==Construction of Turing Machines== ...

...''Early Hand Methods''</ref> by the mathematician and cryptanalyst [[Alan Turing]] at the British [[Government Code and Cypher School]] at [[Bletchley Park] ==Turing's method== ...

The ''ban'' and the ''deciban'' were invented by [[Alan Turing]] with [[Irving John Good|Irving John "Jack" Good]] in 1940, to measure the ...|title=Studies in the History of Probability and Statistics. XXXVII A. M. Turing's statistical work in World War II |journal=[[Biometrika]] |date=1979 |volu ...

...nd Young as the sets <math>\mathrm{NP}^{(k)}</math> of [[nondeterministic Turing machine]] programs <math>p</math> that, for inputs <math>x</math> that they ...ion <math>f</math> such that <math>K_f^k</math> is not paddable.{{r|jy}} [[Alan Selman]] observed that this would imply a simpler conjecture, the ''encrypt ...

...e theory of computation was to prove that the running time of a one-tape [[Turing machine]] is quadratic for accepting a palindromic language and [[sorting a ==={{anchor|Turing machines time complexity}}Turing-machine time complexity=== ...

...ödel sentences]], it is argued that the human mind cannot be computed on a Turing Machine that works on [[Peano axioms|Peano arithmetic]] because the latter ...tive procedure]] that can be simulated in a [[Deterministic Turing machine|Turing machine]]. ...

...[[abstract machine]]''. As an abstract machine, it shares features with [[Turing machine]]s and the [[SECD machine]]. The Krivine machine explains how to co ...ead normal form and to describe formally this process. Like [[Alan Turing|Turing]] used an abstract machine to describe formally the notion of algorithm, [[ ...

...opology of computation, since functions which are equivalent in the Church-Turing sense may still have different topologies. ...utability]] equivalent to [[Μ-recursive_function|general recursion]] and [[Turing machine]]s.<ref name="Barendregt">Barendregt, H.P., The Lambda Calculus Syn ...

...ministic algorithm]] to check a single solution, or for a nondeterministic Turing machine to perform the whole search. "[[Complete (complexity)|Complete]]" r ...olynomial time]]),<ref>{{Cite book| last=Cobham | first=Alan | author-link=Alan Cobham | year = 1965 | chapter = The intrinsic computational difficulty of ...

...em is a mathematical definition of a computer and program, usually via a [[Turing machine]]. The proof then shows, for any program {{var|f}} that might deter ...iven [[programming language]] that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the p ...

...], the class of problems solvable by a deterministic or nondeterministic [[Turing machine]] in polynomial space and unlimited time.<ref>{{cite book |author1= ...to specify a solution succinctly). It can be solved using an [[alternating Turing machine]] in linear time, since [[AP (complexity)|AP]] = PSPACE, where AP i ...

...other conditions that would arise in actual biological systems.<ref name="Turing 1952"/> Second, pioneer [[John von Neumann]] created a [[cellular automaton <ref name="Turing 1952">{{cite journal ...

...Downey|Downey, Rod]] (editor) (2014): ''Turing's Legacy: Developments from Turing's Ideas in Logic''. [[Cambridge University Press]], [[Cambridge, UK|Cambrid ...) (2013): ''[https://books.google.com/books?id=MlsJuSj2OkEC Computability: Turing, Gödel, Church, and Beyond]''. [[MIT Press]], [[Cambridge, Massachusetts]], ...

...://cse.engin.umich.edu/stories/computer-scientists-win-best-paper-award-at-turing-centenary-conference/ |access-date=2023-08-13 |website=Computer Science and ...

...Soon after this, [[David Deutsch]] produced a description for a [[quantum Turing machine]] and designed an [[Deutsch–Jozsa algorithm|algorithm]] created to ...ry]], [[quantum complexity theory]] considers what a theoretical [[Quantum Turing machine|universal quantum computer]] could accomplish without accounting fo ...

...is precisely the difficult core of the [[NP-Hard]] problems. Although a [[Turing reduction]] can get around this issue by trying all values of ''k''. ...lez]],<ref name="Gonzalez 1985" /> and by Martin Dyer and [[Alan M. Frieze|Alan Frieze]]<ref name="Dyer 1985" /> in 1985, the Gon algorithm is basically a ...

...ber of elements of the matroid; in complexity-theoretic terms, this is a [[Turing reduction]]. Two oracles are said to be ''polynomially equivalent'' if they As well as polynomial time Turing reductions, other types of reducibility have been considered as well. In pa ...