The technical details of things like Turing completeness and theories of computability are beyond most of them .

如 图灵 可 计算的完整性和理论的东西的技术细节超出了大多数。

Turing machine takes the intuition conception of feasible computability into strict formality and the Church-Turing Thesis that any feasible computability function is universal Turing machine computability is come into being .

图灵机把关于能行可计算的直观看法变成了严格的形式定义，于是形成了任何能行可计算的函数都是通用 图 灵机 可 计算的这一丘奇-图灵论题。

In this paper the partial recursive function is constructed by Hopfield neural networks . The partial recursive function is equivalent with Turing machine the computability of Hopfield neural networks is therefore equivalent with Turing machine .

本文给出了用Hopfield网 计算部分递归函数的构造 性 证明.由于部分递归函数与 图 灵机等价，故Hopfield网与图灵机等价。