Universal Structures and the logic of Forbidden Patterns
Abstract
Forbidden Patterns Problems (FPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs). However, we show that when the input is connected and belongs to a class which has low tree-depth decomposition (e.g. structure of bounded degree, proper minor closed class and more generally class of bounded expansion) any FPP becomes a CSP. This result can also be rephrased in terms of expressiveness of the logic MMSNP, introduced by Feder and Vardi in relation with CSPs. Our proof generalises that of a recent paper by Nesetril and Ossona de Mendez. Note that our result holds in the general setting of problems over arbitrary relational structures (not just for graphs).
Cite
@article{arxiv.0904.2521,
title = {Universal Structures and the logic of Forbidden Patterns},
author = {Florent R. Madelaine},
journal= {arXiv preprint arXiv:0904.2521},
year = {2015}
}
Comments
25 pages, 3 figures, extended version of conference papers at CSR'06 and CSL'06