超计算：计算能力超过图灵机
Hypercomputation: computing more than the Turing machine
摘要：
由于对丘奇-图灵命题的普遍误解，人们普遍认为图灵机提供了可计算的上界。这是不可能的。超计算这一新领域研究的是能够计算比图灵机更多的计算模型，并提出了它们的含义。在这份报告中，我调查了大量关于超计算的工作，解释了这种非经典模型如何适应经典计算理论，并比较了它们的相对能力。我还研究了这种机器的物理要求，以及在宇宙中可能实现的超计算类型。最后，我将展示超计算的可能性如何削弱哥德尔不完备性定理和柴廷发现算术中的“随机性”的影响。
英文摘要：
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation that can compute more than the Turing machine and addresses their implications. In this report, I survey much of the work that has been done on hypercomputation, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers. I also examine the physical requirements for such machines to be constructible and the kinds of hypercomputation that may be possible within the universe. Finally, I show how the possibility of hypercomputation weakens the impact of Godel's Incompleteness Theorem and Chaitin's discovery of 'randomness' within arithmetic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
