Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the so-called syntactic solution method and abstract GSOS.

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Keywords Automatic sequences, Behavioural differential equations, Bialgebra, Coalgebra, Coinduction, Context-free streams, Linear systems, Streams
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Journal Logical Methods in Computer Science
Hansen, H.H, Kupke, C.A, & Rutten, J.J.M.M. (2017). Stream differential equations: Specification formats and solution methods. Logical Methods in Computer Science, 13(1), 1–51. doi:10.23638/LMCS-13(1:3)2017