Kreutzer, Stephan - On the Parameterized Intractability of Monadic Second-Order Logic

lmcs:785 - Logical Methods in Computer Science, March 26, 2012, Volume 8, Issue 1
On the Parameterized Intractability of Monadic Second-Order Logic

Authors: Kreutzer, Stephan

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.


Source : oai:arXiv.org:1203.3167
DOI : 10.2168/LMCS-8(1:27)2012
Volume: Volume 8, Issue 1
Published on: March 26, 2012
Submitted on: March 2, 2010
Keywords: Computer Science - Logic in Computer Science,F.4.1


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