(Co)Algebraic Characterizations of Signal Flow Graphs

One of the first publications of Prakash Panangaden is about compositional semantics of digital networks, back in 1984. Digital net- works transform streams of input signals to streams of output signals. If the output streams of the components of the network are functions of their input streams, then the behavior of the entire network can be nicely characterized by a recursive stream function. In this paper we consider signal flow graphs, i.e., open synchronous digital networks with feedbacks, obtained by composing amplifiers, mergers, copiers, and de- layers. We give two characterizations of the recursive stream functions computed by signal flow graphs: one algebraic in terms of localization of modules of polynomials, and another coalgebraic in terms of Mealy machines. Our main result is that the two characterizations coincide.

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