Network Algebra [Paperback]

Network algebra considers the algebraic study of networks and their behavior. It approaches the models in a sharp and simple manner. This book takes an integrated view of a broad range of applications, varying from concrete hardware-oriented models to high-level software-oriented models.

Network Algebra considers the algebraic study of networks and theirbehaviour. It contains general results on the algebraic theory ofnetworks, recent results on the algebraic theory of models for parallelprograms, as well as results on the algebraic theory of classical controlstructures. The results are presented in a unified framework of thecalculus of flownomials, leading to a sound understanding of the algebraicfundamentals of the network theory.The term 'network' is used in a broad sense within this book, asconsisting of a collection of interconnecting cells, and two radicallydifferent specific interpretations of this notion of networks are studied.One interpretation is additive, when only one cell is active at a giventime - this covers the classical models of control specified by finiteautomata or flowchart schemes. The second interpretation ismultiplicative, where each cell is always active, covering models forparallel computation such as Petri nets or dataflow networks. Moreadvanced settings, mixing the two interpretations are included as well.Network Algebra will be of interest to anyone interested in networktheory or its applications and provides them with the results needed toput their work on a firm basis. Graduate students will also find thematerial within this book useful for their studies.I. An introduction to Network Algebra.- Brief overview of the key results.- Regular expressions.- Iteration theories.- Flownomials.- Basic results.- Mixed calculi.- Structure of the book.- Acknowledgments.- 1. Network Algebra and its applications.- 1.1 Algebra of finite relations.- 1.2 Basic Network Algebra, BNA.- 1.3 Flownomial expressions.- 1.4 Concrete vs.l“8