Abstract: On the fly synthesis of mediators is a revolutionary approach to the seamless networking of today's and future digital systems that increasingly need be connected. The resulting emergent mediators (or Connectors) adapt the interaction protocols run by the connected systems to let them communicate. However, although the mediator concept has been studied and used quite extensively to cope with many heterogeneity dimensions, a remaining key challenge is to support on-the-fly synthesis of mediators. Towards this end, this paper introduces a theory of mediators for the ubiquitous networking environment. The proposed formal model: (i) precisely characterizes the problem of interoperability between networked systems, and (ii) paves the way for automated reasoning about protocol matching (interoperability) and related mediator synthesis.