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Network Algebra

By: Gheorghe Stefanescu

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Paperback | 12 April 2000

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Paperback
420 Pages

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23.39 x 15.6 x 2.18

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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 netsor 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.

Industry Reviews

"Interesting exercises and problems accompany most of sections. Also some open questions related to this subject are present." (Daniela Marinescu, zbMATH 0956.68002, 2022)

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You Can Find This Book In

Non-Fiction Mathematics Algebra Computing & I.T.Computer Networking & Communications Computer Science Mathematical Theory of Computation Maths for Computer Scientists Applied Mathematics Calculus & Mathematical Analysis Numerical Analysis Computer Programming & Software Development

Algorithms & Data Structures Computer Hardware Network Hardware Engineering & Technology Electronics & Communications Engineering Communications Engineering & Telecommunications

Preface
An introduction to Network Algebra
Brief overview of the key results	p. 3
Network Algebra and its applications	p. 17
Relations, flownomials, and abstract networks
Networks modulo graph isomorphism	p. 57
Algebraic models for branching constants	p. 91
Network behaviour	p. 123
Elgot theories	p. 147
Kleene theories	p. 169
Algebraic theory of special networks
Flowchart schemes	p. 197
Automata	p. 223
Process algebra	p. 249
Data-flow networks	p. 275
Petri nets	p. 305
Towards an algebraic theory for software components
Mixed Network Algebra	p. 323
Related calculi, closing remarks	p. 351
Equivalent BNA presentation (LR-flows)	p. 353
Lifting BNA from connections to networks	p. 359
Demonic relation operators	p. 362
Generating congruences	p. 368
Automata, complements	p. 369
Data-flow networks; checking NA axioms	p. 371
Axiomatizing mixed relations	p. 373
Discats as sysecats	p. 375
Decomposing morphisms in discats	p. 377
Plans as free discats	p. 379
Bibliography	p. 381
List of tables	p. 391
List of figures	p. 393
Index	p. 395
Table of Contents provided by Blackwell. All Rights Reserved.

Network Algebra

At a Glance

Paperback

Industry Reviews

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