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Network Algebra

  • Textbook
  • © 2000

Overview

Authors:
  1. Gheorghe Ştefănescu

    1. Faculty of Mathematics, University of Bucharest, Bucharest, Romainia

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  • APPROACHES THE MODELS IN A SHARP AND SIMPLE MANNER * INTEGRATED VIEW OF A BROAD RANGE OF APPLICATIONS VARYING FROM CONCRETE HARDWARE-ORIENTED MODELS TO HIGH-LEVEL SOFTWARE-ORIENTED MODELS.

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XV
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  2. An introduction to Network Algebra

    1. Front Matter

      Pages 1-1
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    2. Brief overview of the key results

      • Gheorghe Ştefănescu
      Pages 3-16

    3. Network Algebra and its applications

      • Gheorghe Ştefănescu
      Pages 17-53

  3. Relations, flownomials, and abstract networks

    1. Front Matter

      Pages 55-55
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    2. Networks modulo graph isomorphism

      • Gheorghe Ştefănescu
      Pages 57-89

    3. Algebraic models for branching constants

      • Gheorghe Ştefănescu
      Pages 91-121

    4. Network behaviour

      • Gheorghe Ştefănescu
      Pages 123-145

    5. Elgot theories

      • Gheorghe Ştefănescu
      Pages 147-168

    6. Kleene theories

      • Gheorghe Ştefănescu
      Pages 169-194

  4. Algebraic theory of special networks

    1. Front Matter

      Pages 195-195
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    2. Flowchart schemes

      • Gheorghe Ştefănescu
      Pages 197-222

    3. Automata

      • Gheorghe Ştefănescu
      Pages 223-248

    4. Process algebra

      • Gheorghe Ştefănescu
      Pages 249-274

    5. Data-flow networks

      • Gheorghe Ştefănescu
      Pages 275-303

    6. Petri nets

      • Gheorghe Ştefănescu
      Pages 305-319

  5. Towards an algebraic theory for software components

    1. Front Matter

      Pages 321-321
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    2. Mixed Network Algebra

      • Gheorghe Ştefănescu
      Pages 323-350

  6. Back Matter

    Pages 351-401
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Faculty of Mathematics, University of Bucharest, Bucharest, Romainia

    Gheorghe Ştefănescu

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