Ebook: Network Algebra

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.

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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.

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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.
Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Brief overview of the key results....Pages 3-16
Network Algebra and its applications....Pages 17-53
Front Matter....Pages 55-55
Networks modulo graph isomorphism....Pages 57-89
Algebraic models for branching constants....Pages 91-121
Network behaviour....Pages 123-145
Elgot theories....Pages 147-168
Kleene theories....Pages 169-194
Front Matter....Pages 195-195
Flowchart schemes....Pages 197-222
Automata....Pages 223-248
Process algebra....Pages 249-274
Data-flow networks....Pages 275-303
Petri nets....Pages 305-319
Front Matter....Pages 321-321
Mixed Network Algebra....Pages 323-350
Back Matter....Pages 351-401

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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.
Content:
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Brief overview of the key results....Pages 3-16
Network Algebra and its applications....Pages 17-53
Front Matter....Pages 55-55
Networks modulo graph isomorphism....Pages 57-89
Algebraic models for branching constants....Pages 91-121
Network behaviour....Pages 123-145
Elgot theories....Pages 147-168
Kleene theories....Pages 169-194
Front Matter....Pages 195-195
Flowchart schemes....Pages 197-222
Automata....Pages 223-248
Process algebra....Pages 249-274
Data-flow networks....Pages 275-303
Petri nets....Pages 305-319
Front Matter....Pages 321-321
Mixed Network Algebra....Pages 323-350
Back Matter....Pages 351-401
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