Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences
Discrete Mathematics
2015-07-01 v6 Logic in Computer Science
Abstract
Fix an integer h>=1. In the universe of coloured trees of height at most h, we prove that for any graph decision problem defined by an MSO formula with r quantifiers, there exists a set of kernels, each of size bounded by an elementary function of r and the number of colours. This yields two noteworthy consequences. Consider any graph class G having a one-dimensional MSO interpretation in the universe of coloured trees of height h (equivalently, G is a class of shrub-depth h). First, class G admits an MSO model checking algorithm whose runtime has an elementary dependence on the formula size. Second, on G the expressive powers of FO and MSO coincide (which extends a 2012 result of Elberfeld, Grohe, and Tantau).
Keywords
Cite
@article{arxiv.1204.5194,
title = {Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences},
author = {Jakub Gajarsky and Petr Hlineny},
journal= {arXiv preprint arXiv:1204.5194},
year = {2015}
}