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- Church–Turing_thesis abstract "In computability theory, the Church–Turing thesis (also known as the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a combined hypothesis ("thesis") about the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose values are algorithmically computable. In simple terms, the Church–Turing thesis states that a function is algorithmically computable if and only if it is computable by a Turing machine.Several independent attempts were made in the first half of the 20th century to formalize the notion of computability: American mathematician Alonzo Church created a method for defining functions called the λ-calculus, British mathematician Alan Turing created a theoretical model for machines, now called Turing machines, that could carry out calculations from inputs, Austrian-American mathematician Kurt Gödel, with Jacques Herbrand, created a formal definition of a class of functions whose values could be calculated by recursion.All three computational processes (recursion, the λ-calculus, and the Turing machine) were shown to be equivalent—all three approaches define the same class of functions. This has led mathematicians and computer scientists to believe that the concept of computability is accurately characterized by these three equivalent processes.Informally, the Church–Turing thesis states that if some method (algorithm) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine (as well as by a recursively definable function, and by a λ-function). In practical terms, this roughly signifies that it is theoretically possible to emulate all kinds of digital computer hardware with software and vice versa. (See also Turing completeness).Even though the three processes mentioned above proved to be equivalent, the fundamental premise behind the thesis — the notion of what it means for a function to be effectively calculable — is "a somewhat vague intuitive one". Thus, the thesis, although it has near-universal acceptance, cannot be formally proven.".
- Church–Turing_thesis wikiPageID "6854".
- Church–Turing_thesis wikiPageRevisionID "604830212".
- Church–Turing_thesis subject Category:Alan_Turing.
- Church–Turing_thesis subject Category:Computability_theory.
- Church–Turing_thesis subject Category:Philosophy_of_computer_science.
- Church–Turing_thesis subject Category:Theory_of_computation.
- Church–Turing_thesis comment "In computability theory, the Church–Turing thesis (also known as the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a combined hypothesis ("thesis") about the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose values are algorithmically computable.".
- Church–Turing_thesis label "Church-Turing-These".
- Church–Turing_thesis label "Church-Turing-hypothese".
- Church–Turing_thesis label "Church–Turing thesis".
- Church–Turing_thesis label "Hipoteza Churcha-Turinga".
- Church–Turing_thesis label "Tese de Church-Turing".
- Church–Turing_thesis label "Tesi di Church-Turing".
- Church–Turing_thesis label "Tesis de Church-Turing".
- Church–Turing_thesis label "Thèse de Church".
- Church–Turing_thesis label "Тезис Чёрча — Тьюринга".
- Church–Turing_thesis label "チャーチ=チューリングのテーゼ".
- Church–Turing_thesis label "邱奇-图灵论题".
- Church–Turing_thesis sameAs Church%E2%80%93Turing_thesis.
- Church–Turing_thesis sameAs Churchova-Turingova_teze.
- Church–Turing_thesis sameAs Church-Turing-These.
- Church–Turing_thesis sameAs Tesis_de_Church-Turing.
- Church–Turing_thesis sameAs Thèse_de_Church.
- Church–Turing_thesis sameAs Tesi_di_Church-Turing.
- Church–Turing_thesis sameAs チャーチ=チューリングのテーゼ.
- Church–Turing_thesis sameAs 처치-튜링_명제.
- Church–Turing_thesis sameAs Church-Turing-hypothese.
- Church–Turing_thesis sameAs Hipoteza_Churcha-Turinga.
- Church–Turing_thesis sameAs Tese_de_Church-Turing.
- Church–Turing_thesis sameAs Q309157.
- Church–Turing_thesis sameAs Q309157.
- Church–Turing_thesis wasDerivedFrom Church–Turing_thesis?oldid=604830212.