Parallelism or concurrency is one of the fundamental concepts in
computer science. But in spite of its importance, theoretical
methods to handle concurrency are not yet sufficiently developed.
This volume presents a comprehensive study of Mazurkiewicz' trace
theory from an algebraic-combinatorial point of view. This theory
is recognized as an important tool for a rigorous mathematical
treatment of concurrent systems. The volume covers several
different research areas, and contains not only known results but
also various new results published nowhere else. Chapter 1
introduces basic concepts. Chapter 2 gives a straight path to
Ochmanski's characterization of recognizable trace languages and to
Zielonka's theory of asynchronous automata. Chapter 3 applies the
theory of traces to Petri nets. A kind of morphism between nets is
introduced which generalizes the concept of synchronization.
Chapter 4 provides a new bridge between the theory of string
rewriting and formal power series. Chapter 5 is an introduction to
a combinatorial theory of rewriting on traces which can be used as
an abstract calculus for transforming concurrent processes.
General
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