Overview
- Addresses the needs of graduate students, researchers, and practitioners in the field, mathematicians and computer scientists alike
- Presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis
- Describes the state space of a concurrent program, which is described as a higher-dimensional space, the topology of which encodes the essential properties of the system
- Includes supplementary material: sn.pub/extras
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Table of contents (8 chapters)
Keywords
About this book
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 topologyhave 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.
Reviews
“The book under review introduces a more recently developed true-concurrency model, which applies concepts and methods from algebraic topology. … I applaud the authors for having delivered what I believe is the first book in a very promising field. I highly recommend this book to mathematicians specializing in topology and seeking a challenging new application, and to those concurrency theorists who have a firm background in category theory.” (Gerald Lüttgen, Mathematical Reviews, February, 2017)
“The book contains a large number of illustrative examples along with many diagrams that serve to illustrate the ideas and make the book quite easy to follow. Indeed the diagrams are an essential guide to the geometrical ideas on which the book is based. … The book can be recommended to both mathematicians and computer scientists as presentingan introduction to an area where further collaboration could be fruitful.” (J. P. E. Hodgson, Computing Reviews, computingreviews.com, July, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Directed Algebraic Topology and Concurrency
Authors: Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
DOI: https://doi.org/10.1007/978-3-319-15398-8
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-15397-1Published: 11 March 2016
Softcover ISBN: 978-3-319-79217-0Published: 19 April 2018
eBook ISBN: 978-3-319-15398-8Published: 02 March 2016
Edition Number: 1
Number of Pages: XI, 167
Number of Illustrations: 1 b/w illustrations
Topics: Math Applications in Computer Science, Algebraic Topology, Mathematical Logic and Formal Languages, Complexity, Computation by Abstract Devices, Mathematical Applications in Computer Science