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History of the Church–Turing thesis

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❶Bulletin of Symbolic Logic.

1. The Thesis and its History

2. Misunderstandings of the Thesis
By Jack Copeland

Placebo group: The other group took dummy pills (placebo). Both groups also went on a high-fiber, low calorie diet. These were the results of the 12 week study, which was published in The Journal of The American Medical Association (a highly respected scientific journal): Heymsfield, et al.

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In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions.

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When the Church-Turing thesis is expressed in terms of the replacement concept proposed by Turing, it is appropriate to refer to the thesis also as ‘Turing’s thesis’, and as ‘Church’s thesis’ when expressed in terms of one or another of the formal replacements proposed by Church.

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The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a Turing machine. In Church's original formulation (Church , ), the thesis says that real-world calculation can be done. There are various equivalent formulations of the Turing-Church thesis (which is also known as Turing's thesis, Church's thesis, and the Church-Turing thesis). One formulation of the thesis is that every effective computation can be carried out by a Turing machine. Effective Methods.

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The history of the Church–Turing thesis ("thesis") involves the history of the development of the study of the nature of functions whose values are effectively calculable; or, in more modern terms, functions whose . Computable. The Church-Turing Thesis. David Hilbert's tenth problem was to devise an algorithm that tests whether a polynomial has an integral root, i.e., find a process which determines the result in a finite number of operations.