Stream Differential Equations: Specification Formats and Solution Methods

TL;DR

This paper surveys the theory of stream differential equations, focusing on their specification formats, solution methods, and the classes of streams they can define, highlighting connections with abstract GSOS.

Contribution

It provides a comprehensive classification of stream differential equation formats and details the relationship between syntactic solutions and abstract GSOS.

Findings

Classified various stream differential equation formats

Analyzed solution methods and their expressive power

Connected syntactic solutions with abstract GSOS

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.