关于计算时间序列中隐机的存在性
On the existence of hidden machines in computational time hierarchies
摘要：
在可计算的函数中，我们假设有一个充分表达的形式公理系统，有一些全函数，尽管它们是可计算的，并且“直观地”被理解为全的，但它们不能被证明是全的。在这篇文章中，我们表明，这意味着存在一个无限的层次结构的时间复杂度类的代表成员是隐藏的（或未知的）各自的正式公理系统。虽然这些类包含了全部可计算函数，但是对于其中的一些函数，形式公理系统不能将其识别为属于时间复杂度类。这导致关于计算复杂性的形式化的不完整结果。
英文摘要：
Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total, cannot be proved to be total. In this article we show that this implies the existence of an infinite hierarchy of time complexity classes whose representative members are hidden from (or unknown by) the respective formal axiomatic systems. Although these classes contain total computable functions, there are some of these functions for which the formal axiomatic system cannot recognize as belonging to a time complexity class. This leads to incompleteness results regarding formalizations of computational 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。
