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Directed Algebraic Topology and Concurrency

By: Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen

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Directed Algebraic Topology and Concurrency

By: Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen

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.

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Page Count

171

Publisher

Springer

Published Date

ISBN 10

3319153986

ISBN 13

9783319153988

Directed Algebraic Topology and Concurrency

By: Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen

Write a review Read reviews Take a Quiz Solve Book Puzzle

Directed Algebraic Topology and Concurrency

By: Lisbeth Fajstrup,Eric Goubault,Emmanuel Haucourt,Samuel Mimram,Martin Raussen

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

171

Publisher

Springer

Published Date

ISBN 10

3319153986

ISBN 13

9783319153988