Abstract
As systems continue to be interconnected, their collective behavior becomes increasingly difficult to predict. The emergent properties of systems of systems make them powerful, but at the same time make them more difficult to design, assure proper behaviors emerge, operate correctly, and have no new security holes. Learning and adaptation cause additional concerns because emergent behavior patterns simply cannot be fully predicted through the use of traditional system development methods, such as testing and model checking. In addition, self-organization can occur as the individual systems optimize to address inefficiencies in the larger system. Designing for and detecting emergent behavior is something that has not been addressed in current systems development methodologies. This paper gives background on approaches for modeling and verifying emergent behavior and then discusses the use of semi-Boolean algebra as a means for detecting emergence in combined behaviors. Semi-Boolean algebra is a generalization of the Boolean algebra concept obtained by weakening the requirement that any two elements have a common upper bound. An example is given and several ways are described that allow emergent behavior to be detected with this technique.