Abstract
We present an alternative proof of a theorem by Courcelle, Makowski and Rotics [6] which states that problems expressible in MSO1 are solvable in linear time for graphs of bounded rankwidth. Our proof uses a game-theoretic approach and has the advantage of being self-contained. In particular, our presentation does not assume any background in logic or automata theory. Moreover our approach can be generalized to prove other results of a similar flavor, for example, that of Courcelle’s Theorem for treewidth [3,19].
This work is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant RO 927/8. A full version is available at http://arxiv.org/abs/1102.0908.
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Langer, A., Rossmanith, P., Sikdar, S. (2011). Linear-Time Algorithms for Graphs of Bounded Rankwidth: A Fresh Look Using Game Theory. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_49
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DOI: https://doi.org/10.1007/978-3-642-20877-5_49
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