Stream Differential Equations: Specification Formats and Solution Methods

Streams, or innite sequences, are innite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream dierential 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 classication of dierent formats of stream dierential equations, their solution methods, and the classes of streams they can dene. Moreover, we describe in detail the connection between the so-called syntactic solution method and abstract GSOS.