二重递归函数及其分层

Double Recursive Functions and Their Hierarchy

中文摘要:

      本文讨论R.Péter[3]所提出的二重递归函数的性质,给出了二重递归函数的另一种等价刻画,即证明了二重速归函数类就是文[6]中所讨论的Z—分层函数类Z=(?).结合文[6]的结论我们便得到了关于二重递归函数类的一种Grzegorezyk型分层和一种更简单的二重递归模式.

英文摘要:

      This paper discusses the properties of double recursive functions which are defined by R.Peter in [3]. An equivalent characterization of double recursive functions is suggested, which is defined to be the class z = ∪_n∈w z_n of z-hierarchy. Then, a Grzegorczyk type hier-archy of double recursive functions is obtained by means of the results of [6]. Furthermore, the standard double recursion of R.Peter is reduced to a more simple scheme.