停机函数的可计算域
Computable domains of a Halting Function
AI总结：
本研究以递归函数可计算性模型探讨单变量部分递归函数的验证函数构建问题，得出与图灵机范式可互通的结论，提出命令式语言中自指与自验证不构成障碍的新观点。
摘要：
我们探讨了构建一个可验证单变量部分递归函数有定义或无定义的函数的可能性。这是可计算性理论中的一个议题，艾伦·M·图灵（Alan M. Turing）于1936年在其奠基性著作《论可计算数》（On Computable Numbers）中首次对该问题展开研究。本文采用递归函数的可计算性模型而非图灵机来研究该问题，但所得结果可轻松在两种范式间转换。在给定点无定义的递归函数，对应于对给定输入“不会终止”的图灵机。我们提出的观点与传统视角略有偏差：在命令式语言中，自指与自验证问题并非一种障碍。
英文摘要：
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing in 1936 in his foundational work "On Computable Numbers". Here we face it using the Model of computability of the recursive functions instead of the Turing's machines, but the results are transferable from one to another paradigm with ease. Recursive functions that are not defined at a given point, correspond to the Turing machines that "do not end" for a given input. What we propose Is a slight slip from the orthodox point of view: the issue of the self-reference and of the self-validation is not an impediment in imperative languages.
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。
