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As dynamic software architecture use becomes more widespread, a variety of formal specification languages have been developed to gain a better understanding of the foundations of this type of software evolutionary change. In this paper we survey 14 formal specification approaches based on graphs, process algebras, logic, and other formalisms. Our survey will evaluate the ability of each approach to specify self-managing systems as well as the ability to address issues regarding expressiveness and scalability. Based on the results of our survey we will provide recommendations on future directions for improving the specification of dynamic software architectures, specifically self-managed architectures.