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User:Bluedecklibrary/User:Ttanxu/多項式譜系

维基百科,自由的百科全书

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计算复杂性理论多项式谱系是一系列复杂度类,用以从 P, NPco-NP 产生预言机。 它是数理逻辑算数阶层分析阶层的限定资源意义上的对应。

定义

有很多多项式谱系的等价定义。{{Ordered list}}

多项式谱系中的复杂度类的关系

可交换图相当的时间多项式分层结构。 箭头表示。

定义表明了如下的关系:

性质

未解决的计算机科学问题
(更多的未解决计算机科学问题)

Each class in the polynomial hierarchy contains -complete problems (problems complete under polynomial-time many-one reductions). Furthermore, each class in the polynomial hierarchy is closed under -reductions: meaning that for a class C in the hierarchy and a language , if , then as well. These two facts together imply that if is a complete problem for , then , and . For instance, . In other words, if a language is defined based on some oracle in C, then we can assume that it is defined based on a complete problem for C. Complete problems therefore act as "representatives" of the class for which they are complete. [[:Category:序位]] [[:Category:結構複雜度理論]]