Taking it to the limit: on infinite variants of NP-complete problems

T. Hirst, D. Harel
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引用次数: 26

Abstract

Infinite, recursive versions of NP optimization problems are defined. For example, MAX CLIQUE becomes the question of whether a recursive graph contains an infinite clique. The work was motivated by trying to understand what makes some NP problems highly undecidable in the infinite case, while others remain on low levels of the arithmetical hierarchy. Two results are proved; one enables using knowledge about the infinite case to yield implications to the finite case, and the other enables implications in the other direction. Taken together, the two results provide a method for proving (finitary) problems to be outside the syntactic class MAX NP, hence outside MAX SNP too. The technique is illustrated with many examples.<>
求极限:np完全问题的无穷变体
定义了NP优化问题的无限递归版本。例如,MAX CLIQUE变成了递归图是否包含无限团的问题。这项工作的动机是试图理解是什么使得一些NP问题在无限情况下高度不可判定,而另一些问题仍然处于较低的算术层次。证明了两个结果;一种是利用关于无限情况的知识来推导有限情况,另一种是在另一个方向上推导。综合起来,这两个结果提供了一种方法来证明(有限)问题在语法类MAX NP之外,因此也在MAX SNP之外。用许多例子说明了这种技术。
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