Church thesis tutorialspoint

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Is the Turing thesis equivalent to Church's thesis?

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.

What is the axiom CT in Church's thesis?

"Church's thesis" redirects here. For the axiom CT in constructive mathematics, see Church's thesis (constructive mathematics).

How did church come up with his thesis?

Kleene proposes Thesis I: This left the overt expression of a "thesis" to Kleene. In his 1943 paper Recursive Predicates and Quantifiers Kleene proposed his "THESIS I": This heuristic fact [general recursive functions are effectively calculable] ... led Church to state the following thesis.

How did church prove that a function is Turing computable?

Church, Kleene, and Turing proved that these three formally defined classes of computable functions coincide: a function is λ-computable if and only if it is Turing computable, and if and only if it is general recursive.

Last Update: Oct 2021


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