DSPACE (n/sup k/)=VAR(k+1)

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI:10.1109/SCT.1991.160278

Neil Immerman

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引用次数: 6

摘要

证明了在DSPACE(n/sup k/)中图灵机可检验的属性集与最多使用k+1个不同变量的一阶句子的一致序列可描述的属性集是完全相等的。他证明了这也等于一个性质集，可以用一个迭代定义来描述一个有限的k次关系集。这是定理PSPACE=VAR(O(1))的改进。作者提出了一些利用这一结果的方向，以获得描述复杂性中变量数量和量词深度之间的权衡。这有平行复杂性的应用。

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DSPACE (n/sup k/)=VAR(k+1)

The author proves that the set of properties checkable by a Turing machine in DSPACE(n/sup k/) is exactly equal to the set of properties describable by a uniform sequence of first-order sentences using at most k+1 distinct variables. He proves that this is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE=VAR(O(1)). The author suggests some directions for exploiting this result to derive tradeoffs between the number of variables and the quantifier-depth in descriptive complexity. This has applications to parallel complexity.<>

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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