An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree
An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree
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有界度结构的最优Gaifman范式构造
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Nicole Schweikardt
中科院分区：
文献类型：
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作者：
Lucas Heimberg;D. Kuske;Nicole Schweikardt
本文的主要结果提出了3倍指数算法，该算法将一阶公式φ与数字D一起转换为Gaifman正常形式的公式，该公式与最多d的结构d相当多项式生长，我们甚至获得了2倍的指数算法。公式无法避免，对于第3度的结构，由于独立利益而不可避免以Gaifman正常形式形成句子，该句子等效于所有结构。
This paper's main result presents a 3-fold exponential algorithm that transforms a first-order formula φ together with a number d into a formula in Gaifman normal form that is equivalent to φ on the class of structures of degree at most d. For structures of polynomial growth, we even get a 2-fold exponential algorithm. These results are complemented by matching lower bounds: We show that for structures of degree 2, a 2-fold exponential blow-up in the size of formulas cannot be avoided. And for structures of degree 3, a 3-fold exponential blow-up is unavoidable. As a result of independent interest we obtain a 1-fold exponential algorithm which transforms a given first-order sentence φ of a very restricted shape into a sentence in Gaifman normal form that is equivalent to φ on all structures.
DOI：
10.1109/lics.2006.13
发表时间：
2006
期刊：
21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
影响因子：
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作者：
Anuj Dawar;Martin Grohe;Stephan Kreutzer;Nicole Schweikardt
通讯作者：
Nicole Schweikardt