A short introduction to process theory

TL;DR

This paper introduces the fundamentals of process theory, focusing on transition systems, concurrency, composition, and semantics, with connections to automata, programs, and Petri nets to enhance understanding.

Contribution

It provides a comprehensive overview of process behaviour theory, including semantics and laws, and links to related models like automata and Petri nets, advancing foundational understanding.

Findings

Detailed treatment of labelled transition systems

Connections established with automata and Petri nets

Progressive reduction of limitations in process models

Abstract

These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting of transition systems: (i) concurrency and interaction, (ii) abstraction, (iii) sequential composition, alternative composition, and iteration, (iv) expressions that represent process behaviours, and (v) structural operational semantics and equational laws for such expressions. To quicken an intuitive understanding, direct connections with programs and automata are established wherever appropriate. For the interested reader, direct connections with Petri nets are also established. In each chapter, except the last one, it shows that what has been dealt with so far still has certain limitations. Each time, the next chapter is devoted to reducing the limitations concerned.