Church-Turing thesis

In computability theory the Church–Turing thesis (also known as Church's thesis, Church's conjecture and Turing's thesis) is a combined hypothesis about the nature of effectively calculable (computable) functions by recursion (Church's Thesis), by mechanical device equivalent to a Turing machine (Turing's Thesis) or by use of Church's λ-calculus:Church's Thesis: "Every effectively calculable function (effectively decidable predicate) is general recursive" (Kleene 1952:300)Turing's Thesis: "Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX." (Kleene 1952:376)
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