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Directed Algebraic Topology and Concurrency

  • Lisbeth Fajstrup
  • Eric Goubault
  • Emmanuel Haucourt
  • Samuel Mimram
  • Martin Raussen

Table of contents

  1. Front Matter
    Pages i-xi
  2. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 1-5
  3. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 7-23
  4. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 25-56
  5. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 57-90
  6. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 91-104
  7. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 105-127
  8. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 129-150
  9. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
    Pages 151-153
  10. Back Matter
    Pages 155-167

About this book

Introduction

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis.

Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs.

The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account.

The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.

Keywords

ALCOOL Tool Concurrency Theory Directed Algebraic Topology Distributed Networks Geometrical Models for Execution Spaces Higher Dimensional Automata Models for Concurrency State space Reduction Static Analysis of Concurrent Programs

Authors and affiliations

  • Lisbeth Fajstrup
    • 1
  • Eric Goubault
    • 2
  • Emmanuel Haucourt
    • 3
  • Samuel Mimram
    • 4
  • Martin Raussen
    • 5
  1. 1.Department of Mathematical SciencesAalborg UniversityAalborg ØstDenmark
  2. 2.École PolytechniqueGif-sur-YvetteFrance
  3. 3.École PolytechniqueGif-sur-YvetteFrance
  4. 4.École PolytechniqueGif-sur-YvetteFrance
  5. 5.Department of Mathematical SciencesAalborg UniversityAalborg ØstDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15398-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-15397-1
  • Online ISBN 978-3-319-15398-8
  • Buy this book on publisher's site
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