Universal structures and the logic of forbidden patterns

Authors:
Florent Madelaine
Affiliations:
Department of Computer Science, University of Durham, Science Labs, Durham, U.K.
Venue:
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Year:
2006

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Abstract

Forbidden Patterns Problems (FPPs) 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 and 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).