Universal structures and the logic of forbidden patterns

Abstract

Forbidden Patterns Problems (PPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs). However, we show that when the input belongs to a proper minor closed class, a FPP becomes a CSP. This result can also be rephrased in terms of expressiveness of the logic MMSNP, introduced by Feder ami Vardi in relation with CSPs. Our proof generalises that of a recent paper by Nešetřil and Ossona de Mendez. Note that our result holds in the general setting of problems over arbitrary relational structures (not just for graphs). © Springer-Verlag Berlin Heidelberg 2006.