The Resource Directed algebraic topology and concurrency, Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
Directed algebraic topology and concurrency, Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
 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 wellknown 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 higherdimensional 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
 Language
 eng
 Extent
 1 online resource (xi, 167 pages)
 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
 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
 4.2.4 Simple Programs with Mutexes; 4.2.5 DHomotopy; 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
 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
 7.2.1 Contractibility of Restricted Path Spaces; 7.2.2 Presimplicial Sets and the Nerve Theorem; 7.2.3 Path Space as a ProdSimplicial Complex; 8 Perspectives; References; Index
 Isbn
 9783319153988
 Label
 Directed algebraic topology and concurrency
 Title
 Directed algebraic topology and concurrency
 Statement of responsibility
 Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
 Language
 eng
 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 wellknown 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 higherdimensional 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
 Cataloging source
 GW5XE
 Dewey number
 004.01/51
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA76.9.M35
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Label
 Directed algebraic topology and concurrency, Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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
 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
 4.2.4 Simple Programs with Mutexes; 4.2.5 DHomotopy; 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
 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
 7.2.1 Contractibility of Restricted Path Spaces; 7.2.2 Presimplicial Sets and the Nerve Theorem; 7.2.3 Path Space as a ProdSimplicial Complex; 8 Perspectives; References; Index
 Control code
 ocn944178213
 Dimensions
 unknown
 Extent
 1 online resource (xi, 167 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319153988
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319153988
 Other physical details
 illustration
 Quality assurance targets
 unknown
 http://library.link/vocab/recordID
 .b35297396
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)944178213
 springer3319153986
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