On the traces* concatenation of infinite

There is a straightforward generalization of traces to infinite traces as dependence graphs where every vertex has finitely many predecessors, or what is the same, as a backward closed and directed set of traces with respect to prefix ordering. However, this direct approach has a drawback since it does not allow one to describe some basic phenomena which are related to concatenation. We solve this problem by adding to an infinite trace a second component. This second component is a finite alphabetic information which is called the alphabet at injnity. We obtain a compact and complete ultra-metric space where the concatenation is uniformly continuous and where the set of finite traces is an open, discrete, and dense subset. Our objects arise in a natural way from the consideration of dependence graphs where the induced partial order is well-founded. Such a graph splits into a so-called real part and a transjnite part. From the transfinite part only its alphabet is of importance. Our approach is a nontrivial generalization of the well-known construction for words and yields a convenient semantics for infinite concurrent processes.