论物理系统的计算能力第II部分：与传统计算机科学的关系
On the computational capabilities of physical systems part II: relationship with conventional computer science
摘要：
在这两篇论文的第一篇中，我们证明了没有一台物理计算机能够正确地完成所有的计算任务。这个结果的普遍性来自于它使用了一个新的计算定义，“物理计算”。这两篇论文中的第二篇阐述了与物理计算相关的数学结构和不可能结果。类似的乔姆斯基层次结构的结果，有关通用图灵机和Halting定理的推导，是有关某些种类的纠错码的（不）可能性的结果。此外，一个类似的算法信息的复杂性，“预测复杂性”，阐述。一个独立于任务的界限是根据计算任务的预测复杂性对于两个用于解决该任务的不同通用物理计算机可以有多大差异而得出的，这个界限类似于“编码”界限，该界限控制图灵机计算的算法信息复杂性对于两个通用图灵机可以有多大差异。最后，证明了要么我们宇宙的哈密顿量限制了某种类型的计算，要么预测复杂度是唯一的（不像算法信息复杂度）。
英文摘要：
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of computation, ``physical computation''. This second paper of the pair elaborates the mathematical structure and impossibility results associated with physical computation. Analogues of Chomsky hierarcy results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, ``prediction complexity'', is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different universal physical computers used to solve that task, a bound similar to the ``encoding'' bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity).
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。
