Recognizable sets of graphs, hypergraphs and relational structures: A survey

Abstract

New results on the recognizability of sets of finite graphs, hypergraphs and relational structures are presented. The general framework of this research which associates tightly algebraic notions (equational and recognizable sets) and Monadic Second-Order logic (for defining sets and transformations-of graphs, hypergraphs and relational structures) is reviewed. The lecture [3] is based on two submitted but nevertheless available articles [1,4]; the present text is an informal overview. The numerous definitions and results can be found in the two articles. © Springer-Verlag Berlin Heidelberg 2004.