This dissertation proposes a formal theory of interoperability that explains 1) what interoperability is as opposed to how it works, 2) how to tell whether two or more systems can interoperate and 3) how to identify whether systems are interoperating or merely exchanging bits and bytes. The research provides a formal model of data in M&S that captures all possible representations of a real or imagined thing and distinguishes between existential dependencies and transformational dependencies. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally specify interoperation, the ability to exchange information, as a necessary condition for interoperability. Theorems of interoperation that capture the nature and boundaries of the interoperation space and how to measure it are formulated. Interoperability is formally captured as a subset of the interoperation space for which transformational dependencies can be fulfilled. Theorems of interoperability that capture the interoperability space and how to measure it are presented.
Using graph theory and complexity theory, the model of data is reformulated as a graph, and the complexity of interoperation and interoperability is shown to be at least NP-Complete. Model Based Data Engineering (MBDE) is formally defined using the model of data introduced earlier and transformed into a heuristic that supports interoperability. This heuristic is shown to be more powerful than current approaches in that it is consistent and can easily be verified
