Stream differential equations
Specification formats and solution methods
Helle Hvid Hansen (TU Delft - Energy and Industry, Centrum Wiskunde & Informatica (CWI))
Clemens Kupke (University of Strathclyde)
Jan Rutten (Centrum Wiskunde & Informatica (CWI), Radboud Universiteit Nijmegen)
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Abstract
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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