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Heterogeneity is a challenge to overcome in the design of embedded systems. We presented in the recent past a theory for the composition of heterogeneous components based on tagged systems, a behavioral (denotational) framework. in this paper, we present an operational view of tagged systems, where we focus on tag machines as mathematical artifacts that act as finitary generators of tagged systems. Properties of tag machines are investigated. A fundamental theorem on homogeneous compositionality is given as a first step towards an operational theory of heterogeneous systems.