This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. SDSs are a class of discrete dynamical systems which are a significant generalization of cellular automata and provide a new general theory of discrete computer simulations. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS.

Starting from a broad range of topics on structure theory, thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook relevant to applied mathematicians and computer scientists alike.

Inhalt

What is a Sequential Dynamical System?.- A Comparative Study.- Graphs, Groups, and Dynamical Systems.- Sequential Dynamical Systems over Permutations.- Phase-Space Structure of SDS and Special Systems.- Graphs, Groups, and SDS.- Combinatorics of Sequential Dynamical Systems over Words.- Outlook.