On the Parameterised Intractability of Monadic Second-Order Logic
| dc.creator | Kreutzer, Stephan | |
| dc.date | 2009-04-08 | |
| dc.date.accessioned | 2026-07-07T13:01:42Z | |
| dc.date.available | 2026-07-07T13:01:42Z | |
| dc.description | 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. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1302 | |
| dc.identifier | http://arxiv.org/abs/0904.1302 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226234 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Computational Complexity | |
| dc.title | On the Parameterised Intractability of Monadic Second-Order Logic | |
| dc.type | text |