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The Church-Turing Thesis (Stanford Encyclopedia of Philosophy)
Nachum Dershowitz and Yuri Gurevich. July The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates about algorithmic computation. Here, we prove that augmenting those postulates with an additional requirement regarding basic operations implies Church's Thesis, namely, that the only numeric functions that can be calculated by effective means are the recursive ones which are the same, extensionally, as the Turing-computable numeric functions.
In computer science and quantum physics , the Church—Turing—Deutsch principle CTD principle is a stronger, physical form of the Church—Turing thesis formulated by David Deutsch in The principle was stated by Deutsch in with respect to finitary machines and processes. He observed that classical physics , which makes use of the concept of real numbers , cannot be simulated by a Turing machine , which can only represent computable reals. Deutsch proposed that quantum computers may actually obey the CTD principle, assuming that the laws of quantum physics can completely describe every physical process.
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