Network Algebra
Gheorghe Ştefănescu (Author), Gheorghe ÷Stefæanescu (Author)
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
1 online resource (XVI, 402 p. 1 illus.).
9781447104797, 144710479X
1058429618
I. An introduction to Network Algebra
Brief overview of the key results
1. Network Algebra and its applications
II. Relations, flownomials, and abstract networks
2. Networks modulo graph isomorphism
3. Algebraic models for branching constants
4. Network behaviour
5. Elgot theories
6. Kleene theories
7. Flowchart schemes
8. Automata
9. Process algebra
10. Data-flow networks
11. Petri nets
IV. Towards an algebraic theory for software components
12. Mixed Network Algebra
Related calculi, closing remarks
Appendix B: Lifting BNA from connections to networks
Appendix C: Demonic relation operators
Appendix D. Generating congruences
Appendix E: Automata, complements
Appendix F: Data-flow networks; checking NA axioms
Appendix G: Axiomatizing mixed relations
Appendix H: Discats as sysecats
Appendix I: Decomposing morphisms in discats
Appendix J: Plans as free discats
List of tables
List of figures
English
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