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R. Ganian, J. Obdrálek:
"Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes";
Talk: International Workshop on Combinatorial Algorithms (IWOCA), Rouen, France; 2013-07-10 - 2013-07-12; in: "Combinatorial Algorithms - 24th International Workshop", T. Lecroq, L. Mouchard (ed.); Springer / LNCS, 8288 (2013), ISBN: 978-3-642-45277-2; 164 - 177.

We combine integer linear programming and recent advances
in Monadic Second-Order model checking to obtain two new algorithmic
meta-theorems for graphs of bounded vertex-cover. The first one shows
that the model checking problem for cardMSO1, an extension of the
well-known Monadic Second-Order logic by the addition of cardinality
constraints, can be solved in FPT time parameterized by vertex cover.
The second meta-theorem shows that the MSO partitioning problems
introduced by Rao can also be solved in FPT time with the same parameter.
The significance of our contribution stems from the fact that these formalisms
can describe problems which are W[1]-hard and even NP-hard
on graphs of bounded tree-width. Additionally, our algorithms have only
elementary dependence on the parameter and formula. We also show
that both results are easily extended from vertex cover to neighborhood
diversity.

MSO model checking, parameterized complexity, vertex cover, integer linear programming

Project Head Stefan Szeider:
The Parameterized Complexity of Reasoning Problems