2-Testability and Relabelings Produce Everything

We show that grammar systems with communication by command and with extremely simple rewriting rules (in fact, only relabelings are needed) are able to generate all recursively enumerable languages. The result settles several open problems in the area of grammar systems. We also present the result in a general framework, without referring to grammar systems, obtaining a characterization of recursively enumerable languages from a new point of view.