On the Parameterised Intractability of Monadic Second-Order Logic

Details On the Parameterised Intractability of Monadic Second-Order Logic On the Parameterised Intractability of Monadic Second-Order Logic

2009-04-08

arxiv.org/abs/0904.1302v1

Computer Science

Logic in Computer Science

23 pages

Scientific paper

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 is fixed-parameter tractable on C by linear time parameterised algorithms. 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 can not 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 such that the tree-width of C is not bounded by log^{16}(n) then MSO_2-model checking is not fixed-parameter tractable unless the satisfiability problem SAT for propositional logic 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 fixed-parameter tractable unless all problems in the polynomial-time hierarchy, and hence in particular all problems in NP, can be solved in sub-exponential time.

Affiliated with

Also associated with

No associations

Rating

On the Parameterised Intractability of Monadic Second-Order Logic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Parameterised Intractability of Monadic Second-Order Logic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Parameterised Intractability of Monadic Second-Order Logic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-214402