文章基本信息

标题：On the Parameterized Intractability of Monadic Second-Order Logic
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作者：Stephan Kreutzer
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2012
卷号：8
期号：1
页码：1
DOI：10.2168/LMCS-8(1:27)2012
出版社：Technical University of Braunschweig
摘要：One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms, where the parameter is the tree-width plus the size of the formula. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem cannot be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions and is such that the tree-width of C is not bounded by \log^{84} n then MSO_2-model checking is not fpt unless SAT can be solved in sub-exponential time. If the tree-width of C is not poly-logarithmically bounded, then MSO_2-model checking is not fpt unless all problems in the polynomial-time hierarchy can be solved in sub-exponential time.
其他关键词：Parameterized Complexity, Algorithmic Meta-Theorems, Finite Model Theory