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Hypercomputation : ウィキペディア英語版 | Hypercomputation Hypercomputation or super-Turing computation refers to models of computation that go beyond Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions. The term "super-Turing computation" first appeared in talks, the PhD thesis,〔 〕 and even earlier technical reports of Hava Siegelmann since the early 1990s for a very particular theory (described below) and became a subfield of computation since her seminal 1995 ''Science'' paper.〔 (Work received wide media attention, and was mentioned as founding the field of HyperComputation.)〕 The term "hypercomputation" was introduced in 1999 by Jack Copeland and Diane Proudfoot.〔Copeland and Proudfoot, ''(Alan Turing's forgotten ideas in computer science )''. Scientific American, April 1999〕 The terms are not quite synonymous: "super-Turing computation" by Siegelmann usually implies that the proposed model is likely to exist in nature (via biology and/or physics) and may thus be physically realizable, while "hypercomputation" may be a general mathematical or philosophical idea. ==History== A computational model going beyond Turing machines was introduced by Alan Turing in his 1938 PhD dissertation ''Systems of Logic Based on Ordinals''.〔Alan Turing, 1939, ''Systems of Logic Based on Ordinals'' Proceedings London Mathematical Society Volumes 2–45, Issue 1, pp. 161–228.()〕 This paper investigated mathematical systems in which an oracle was available, which could compute a single arbitrary (non-recursive) function from naturals to naturals. He used this device to prove that even in those more powerful systems, undecidability is still present. Turing's oracle machines are mathematical abstractions, and are not physically realizable.〔"Let us suppose that we are supplied with some unspecified means of solving number-theoretic problems; a kind of oracle as it were. We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine" (Undecidable p. 167, a reprint of Turing's paper ''Systems of Logic Based On Ordinals'')〕
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