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).

Source : oai:arXiv.org:1204.5194

DOI : 10.2168/LMCS-11(1:19)2015

Volume: Volume 11, Issue 1

Published on: April 1, 2015

Submitted on: January 20, 2014

Keywords: Computer Science - Discrete Mathematics,Computer Science - Logic in Computer Science

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