对角方法与超计算
The Diagonal Method and Hypercomputation
摘要：
对角线方法经常被用来表明图灵机不能解决自己的停机问题。最近有几次尝试表明，这种方法也暴露了其他理论计算模型中的矛盾或任意性，这些理论模型声称能够解决图灵机的停机问题。我们表明，这样的论点是有缺陷的-矛盾只发生在一种类型的机器可以计算自己的对角函数。然后，我们证明了为什么这种情况不会发生的超计算的方法受到攻击，为什么它不太可能发生在任何其他严重的方法。
英文摘要：
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation that claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed -- a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation does not occur for the methods of hypercomputation under attack and why it is unlikely to occur in any other serious methods.
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