1 Searching for flexible repeated patterns using a non transitive similarity relation. Henri Soldano, Laboratoire d'Informatique de Paris Nord, URA-CNRS 1507, Institut Galilée, Université Paris Nord, Av. J.B. Clément, 93430 Villetaneuse, France, and Atelier de Bio-Informatique, section Physique-Chimie, Institut Curie, 11 rue Pierre et Marie Curie, 75005 Paris, France Alain Viari, Laboratoire de Physique et Chimie Biomoléculaires, URA-CNRS 198 and Atelier de Bio-Informatique, section Physique-Chimie, Institut Curie. Marc Champesme Laboratoire d'Informatique de Paris Nord, URA-CNRS 1507, Institut Galilée, Université Paris Nord, and Atelier de Bio-Informatique, section Physique-Chimie, Institut Curie. Abstract. Given a reflexive and symmetric, but not necessarily transitive, similarity relation defined on an alphabet of symbols, two objects of size k are related if, in each position, their symbols are related. Then, given a set of objects we are interested in maximal subsets of related objects. We give some general properties of these subsets and we propose algorithms for identifying them in the particular case of k-length substrings in a string. These algorithms derive from the Karp, Miller and Rosenberg algorithms for identification of repeated patterns. Introduction. In a previous work Karp and al. (1972) have proposed various algorithms, hereafter referred to as KMR algorithms, to identify repeated patterns in a structure of size N (string, array or tree). In their approach the patterns to identify correspond to exact matches between objects. For instance, two k-length substrings match if, in each position, the same symbol is present in both substrings. However some situations require a more flexible matching and patterns corresponding to similar, rather than strictly identical, objects are searched for. As an example, in molecular biology similar fragments of amino acid sequences may exhibit a similar 3D-structure or biological