Equivalence of Structural Knowledges in Distributed Algorithms

Distributed algorithms correctness usually relies upon th e use of some knowledge about the underlying network (a specific topology , some metrics,...). We define equivalent structural knowledges to be such knowledges that can be computed distributively one knowing the other. W present a combinatorial characterization of this equivalence. Some app lications are also given: zero knowledge, classical metrics (size, diameter, ...). This characterization is defined in terms of graphs covering s and quasicoverings. The proofs are based upon an algorithm proposed b y A. Mazurkiewicz, and on techniques of termination detection by Shy, Szy manski, and Prywes.