| Description |
1 online resource (xi, 167 pages) : illustration |
| Contents |
Foreword; Preface; Contents; 1 Introduction; 2 A Toy Language for Concurrency; 2.1 A Toy Language; 2.2 Semantics of Programs; 2.2.1 Graphs; 2.2.2 The Transition Graph; 2.2.3 Operational Semantics; 2.3 Verifying Programs; 2.3.1 Correctness Properties; 2.3.2 Reachability in Concurrent Programs; 3 Truly Concurrent Models of Programs with Resources; 3.1 Modeling Resources in the Language; 3.1.1 Taming Concurrency; 3.1.2 Extending the Language with Resources; 3.2 State Spaces for Conservative Resources; 3.2.1 Conservative Programs; 3.2.2 Transition Graphs for Conservative Programs |
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3.3 Asynchronous Semantics; 3.3.1 Toward True Concurrency; 3.3.2 Asynchronous Semantics; 3.3.3 Coherent Programs; 3.3.4 Programs with Mutexes Only; 3.4 Cubical Semantics; 3.4.1 Precubical Sets; 3.4.2 The Geometric Realization; 3.5 Historical Notes; 4 Directed Topological Models of Concurrency; 4.1 Directed Spaces; 4.1.1 A Definition; 4.1.2 Limits and Colimits; 4.1.3 Directed Geometric Semantics; 4.1.4 Simple Programs; 4.2 Homotopy in Directed Algebraic Topology; 4.2.1 Classical Homotopy Theory; 4.2.2 Homotopy Between Directed Paths in Dimension 2; 4.2.3 Dihomotopy and the Fundamental Category |
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4.2.4 Simple Programs with Mutexes; 4.2.5 D-Homotopy; 4.3 Constructions on the Fundamental Category; 4.3.1 The Seifert -- Van Kampen Theorem; 4.3.2 The Universal Dicovering Space; 4.4 Historical Notes and Other Models; 5 Algorithmics on Directed Spaces; 5.1 The Boolean Algebra of Cubical Regions; 5.2 Computing Deadlocks; 5.3 Factorizing Programs; 6 The Category of Components; 6.1 Weak Isomorphisms; 6.1.1 Systems of Weak Isomorphisms; 6.1.2 A Maximal System; 6.1.3 Quotienting by Weak Isomorphisms; 6.1.4 Other Definitions; 6.2 Examples of Categories of Components; 6.2.1 Trees |
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6.2.2 Cubical Regions in Dimension 2; 6.2.3 The Floating Cube and Cross; 6.3 Computing Components; 6.3.1 The Case of One Hole; 6.3.2 The General Case; 6.3.3 The Seifert -- Van Kampen Theorem; 6.4 Historical Notes, Applications, and Extensions; 6.4.1 Categories with Loops; 6.4.2 Past and Future Components; 7 Path Spaces; 7.1 An Algorithm for Computing Components of Trace Spaces; 7.1.1 Path Spaces for Simple Programs; 7.1.2 The Index Poset; 7.1.3 Determination of Dipath Classes; 7.1.4 An Efficient Implementation; 7.2 Combinatorial Models for Path Spaces |
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7.2.1 Contractibility of Restricted Path Spaces; 7.2.2 Presimplicial Sets and the Nerve Theorem; 7.2.3 Path Space as a Prod-Simplicial Complex; 8 Perspectives; References; Index |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Online resource; title from PDF title page (SpringerLink, viewed March 9, 2016) |
| Subject |
Computer multitasking -- Mathematics
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Algebraic topology.
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Algebraic topology.
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Mathematical theory of computation.
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Cybernetics & systems theory.
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User interface design & usability.
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Mathematical modelling.
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Maths for computer scientists.
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COMPUTERS -- Computer Literacy.
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COMPUTERS -- Computer Science.
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COMPUTERS -- Data Processing.
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COMPUTERS -- Hardware -- General.
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COMPUTERS -- Information Technology.
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COMPUTERS -- Machine Theory.
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COMPUTERS -- Reference.
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Algebraic topology
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| Form |
Electronic book
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| Author |
Fajstrup, Lisbeth, author.
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Goubault, Eric, author.
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Haucourt, Emmanuel, author.
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Mimram, Samuel, 1983- author.
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Raussen, Martin, 1954- author.
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| ISBN |
9783319153988 |
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3319153986 |
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