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Hypergraph Operations, and Logi al Types A. Blumensath 1 Universität Darmstadt Fa hberei h Mathematik, AG 1 S hloÿgartenstraÿe 7 64289 Darmstadt Germany B. Cour elle LaBRI Bordeaux 1 University 351, Cours de la Libération 33405 Talen e edex Fran e Abstra t We study several algebras of graphs and hypergraphs and the orresponding notions of equational sets and re ognizable sets. We generalize and unify several existing results whi h ompare the asso iated equational and re ognizable sets. The basi algebra on relational stru tures is based on disjoint union and quanti er-free de nable operations. We expand it to an equivalent one by adding operations de nable with few quanti ers , i.e., operations that take into a ount lo al information about elements or tuples. We also onsider monadi se ond-order transdu tions and we prove that the inverse image of a re ognizable set under su h a transdu tion is re ognizable.