As simulations have evolved over the last two decades, interoperability between them has emerged as a fundamental technique for increasing their applicability and minimizing the cost of developing and maintaining them. From totally independent systems, to manual interfaces, automated interfaces, messaging standards, control standards, and architectural standards, the field has been transformed from a set of independent programs to a loose confederation working together to maximize each others investments. In the future, simulation value will be measured by the degree of interoperability that can be attained.

Many efforts to realize broad interoperability have been pursued, each with an increasing degree of ambitiousness. We are now envisioning systems and architectures that can support the connection of all types of simulators and are reaching into the broader realm of C4I systems. This paper will define many of the dimensions of interoperability as they exist today, as are planned for the near future, and as could ultimately be achieved. Twelve dimensions will be enumerated and an algebra defined to aid in describing the relationships and the implications of extending interoperability into the different combinations of these dimensions. This algebra is motivated from the DEVS Formalism originally developed in the book Theory of Modelling and Simulation. Graphical portrayals will also be explored as tools to aid in communicating the concepts. The paper champions a structured approach that lays a foundation to support future growth, realizing that the capabilities envisioned today do not encompass the dreams of tomorrow.