| 摘要: |
| 本文引进一种O(F)—LOOP算子,通过该算子可对一般递归函数集进行分层,且该算子对应于计算复杂性中的加速定理,由此我们得到加速度理的定量描述。 |
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| 基金项目:国家自然科学基金 |
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| SPEED—UP THEOREM AND HIERARCHY OF THE RECURSIVE FUNCTIONS |
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Xu Shurun,Wang Yongge
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| Abstract: |
| In this paper , we ll introduce a kind of O(F)-LOOP operator , which will lead to a hierarchy of any recursive functions:O(F)=O(F)n. We've proved that this hierarchy, corresponds to the speed-up theorem , i. e. given any r(x)∈O(F)i, there is a language having O(F)i+1 complexity which can be speeded up by r(x), and also there is a r(x) in O(F)i, so that any language having O(F)i complexity cannot be speeded up by r(x) . Through this, we can grasp the soul of Speed-up theorem in a more higher level. |
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