Assertion: church's function | /r/HasProperty | computable
Facets:
value: by turing machine
type: OTHER
Source sentences:
text: Before the precise definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil methods.
text: His argument relies on a definition of algorithm broader than the ordinary one, so that non-computable functions obtained from some inductive Turing machines are called computable.
text: 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.
text: It may also be shown that a function which is computable ['reckonable'] in one of the systems S i , or even in a system of transfinite type, is already computable [reckonable] in S 1 .
text: To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude "by the Church–