二类可行泛函没有递归公理化

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-06-22 DOI:10.1109/LICS.1992.185541

Anil Seth

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引用次数: 18

摘要

作者给出了一类二类可行泛函C/ sub2 /，它满足Cook的条件，(1990)，不能表示为一类多时函数的lambda闭包和任何递归可枚举的二类可行泛函集。此外，包含此类的总类型二函数的任何类都不能表示为递归可枚举的二类总可计算函数和一类多时间函数集合的lambda闭包。C/sub 2/的定义为C/sub 2/的泛函提供了一个清晰的计算过程。利用C/ sub2 /类泛函，可以引入两个任意一类函数之间的多项式时间可约性的更一般的概念。

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There is no recursive axiomatization for feasible functionals of type 2

The author shows a class of type-two feasible functionals, C/sub 2/, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C/sub 2/ provides a clear computational procedure for functionals of C/sub 2/. Using functionals of class C/sub 2/ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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