# Network Algebra

• Gheorghe Ştefănescu
Book

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

1. Front Matter
Pages I-XV
2. ### An introduction to Network Algebra

1. Front Matter
Pages 1-1
2. Gheorghe Ştefănescu
Pages 3-16
3. Gheorghe Ştefănescu
Pages 17-53
3. ### Relations, flownomials, and abstract networks

1. Front Matter
Pages 55-55
2. Gheorghe Ştefănescu
Pages 57-89
3. Gheorghe Ştefănescu
Pages 91-121
4. Gheorghe Ştefănescu
Pages 123-145
5. Gheorghe Ştefănescu
Pages 147-168
6. Gheorghe Ştefănescu
Pages 169-194
4. ### Algebraic theory of special networks

1. Front Matter
Pages 195-195
2. Gheorghe Ştefănescu
Pages 197-222
3. Gheorghe Ştefănescu
Pages 223-248
4. Gheorghe Ştefănescu
Pages 249-274
5. Gheorghe Ştefănescu
Pages 275-303
6. Gheorghe Ştefănescu
Pages 305-319
5. ### Towards an algebraic theory for software components

1. Front Matter
Pages 321-321
2. Gheorghe Ştefănescu
Pages 323-350
6. Back Matter
Pages 351-401

### Introduction

Network Algebra considers the algebraic study of networks and their behaviour. It contains general results on the algebraic theory of networks, recent results on the algebraic theory of models for parallel programs, as well as results on the algebraic theory of classical control structures. The results are presented in a unified framework of the calculus of flownomials, leading to a sound understanding of the algebraic fundamentals of the network theory. The term 'network' is used in a broad sense within this book, as consisting of a collection of interconnecting cells, and two radically different specific interpretations of this notion of networks are studied. One interpretation is additive, when only one cell is active at a given time - this covers the classical models of control specified by finite automata or flowchart schemes. The second interpretation is multiplicative, where each cell is always active, covering models for parallel computation such as Petri nets or dataflow networks. More advanced settings, mixing the two interpretations are included as well. Network Algebra will be of interest to anyone interested in network theory or its applications and provides them with the results needed to put their work on a firm basis. Graduate students will also find the material within this book useful for their studies.

### Keywords

Concurrency and Control Feedback Network Algebra algebra calculus parallel computation

#### Authors and affiliations

• Gheorghe Ştefănescu
• 1
1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomainia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-0479-7
• Copyright Information Springer-Verlag London Limited 2000
• Publisher Name Springer, London
• eBook Packages
• Print ISBN 978-1-85233-195-5
• Online ISBN 978-1-4471-0479-7