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DOI:
:1994.5(3):55-64

Grzegorczyk分层的一种延伸
郑锡忠,钱磊
(南京大学,南京 210008;南京航空学院,南京 210016)
AN EXTENSION OF Grzegorczyk's HIERARCHY
Zheng Xizhong,Qian Lei
()
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Received:July 22, 1991    Revised:December 21, 1991
> 中文摘要: 本文讨论某些递归函数类的分层问题.首先给出的是原始的Gorzegorczyk分层的一种较为简单的等价定义.然后,作为对Ackermann函数的一种推广,定义了一个递归函数序列{An∈ω.并以此作为分层函数列定义了一种新的递归分层{Zn∈ω(即Z—分层),这种分层涉及了比原始递归函数类更大的一个违归函数类.实际上,原始递归函数类仅是Z—分层的第一层Z.而且这种分层的任意的第n+1层都含
Abstract:This paper discusses the hierarchies of some classes of recursive functions. A simple equivalent definition of original Grzegorczyk's hierarchy is presented at first. Then the authors define by the generalization of Ackermann's function a sequence of recursive functions {An∈ω, based on which they define hierarchy, {Zn∈ω(the Z-hierarchy)of a class of recursive functions which is much larger than the class of primitive recursive functions.The first level Z of this hierarchy is just the class of primitive recursive functions.For all n, Zn+1 contains the universal function of its predecessor Zn. A refinement {Zin,i∈ωof Z-hierarchy is defined at last by the natural hierarchy of each Zn. The refinement on ZO is same as the original Grzegorczyk's hierarchy. This shows that their Z-hierarchy and its refinement are really a natural extension of Grzegorczyk's hierarchy.
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基金项目:国家自然科学基金 国家自然科学基金
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郑锡忠,钱磊.Grzegorczyk分层的一种延伸.软件学报,1994,5(3):55-64

Zheng Xizhong,Qian Lei.AN EXTENSION OF Grzegorczyk's HIERARCHY.Journal of Software,1994,5(3):55-64