Holographic Trees

It is known that computations of anonymous networks can be reduced to the construction of a certain graph, the minimum base of the network. The crucial step of this construction is the inference of the minimum base from a finite tree that each processor can build (its truncated view). We isolate those trees that make this inference possible, and call them holographic. Intuitively, a tree is holographic if it is enough self-similar to be uniquely extendible to an infinite tree. This possibility depends on a size function for the class of graphs under examination, which we call a holographic bound for the class. Holographic bounds give immediately, for instance, bounds for the quiescence time of selfstabilizing protocols. In this paper we give weakly tight holographic bounds for some classes of graphs.