Directed Algebraic Topology and Concurrency
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
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Directed Algebraic Topology and Concurrency
Directed Algebraic Topology and Concurrency
Lisbeth Fajstrup Eric Goubault Emmanuel Haucourt Samuel Mimram Martin Raussen •
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Directed Algebraic Topology and Concurrency
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Lisbeth Fajstrup Department of Mathematical Sciences Aalborg University Aalborg Denmark
Samuel Mimram École Polytechnique Palaiseau France Martin Raussen Department of Mathematical Sciences Aalborg University Aalborg Denmark
Eric Goubault École Polytechnique Palaiseau France Emmanuel Haucourt École Polytechnique Palaiseau France
ISBN 978-3-319-15397-1 DOI 10.1007/978-3-319-15398-8
ISBN 978-3-319-15398-8
(eBook)
Library of Congress Control Number: 2015960769 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by SpringerNature The registered company is Springer International Publishing AG Switzerland
Foreword
Computer science has a rugged tradition of appropriating concepts and mechanisms from classical mathematics, concepts once proudly considered pure and useless, and adapting those concepts to describe and analyze phenomena that once could not have been imagined. Today, the most abstract discoveries of number theory form the foundations of modern cryptography and finance, graph theory lies at the heart of communication networks, social networks, and search structures, and advanced probability has myriad of everyday applications. This book, too, presents novel adaptations and applications of basic concepts from combinatorial and algebraic topology: in this case, paths and their homotopies. The intuition is appealing: one can visualize an execution of a concurrent, two-process program as a path winding its way through a planar region, where progress by one process nudges the arrow along the x-axis, and progress by the other along the y-axis. Certain regions of the plane are forbidden: they correspond to zones of mutual exclusion. Two execut
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