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

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
Contributor
Author
Subject
Genre
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 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
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
http://library.link/vocab/relatedWorkOrContributorDate
  • 1983-
  • 1954-
http://library.link/vocab/relatedWorkOrContributorName
  • Fajstrup, Lisbeth
  • Goubault, Eric
  • Haucourt, Emmanuel
  • Mimram, Samuel
  • Raussen, Martin
http://library.link/vocab/subjectName
  • Computer multitasking
  • Algebraic topology
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • COMPUTERS
  • Algebraic topology
  • Computer Science
  • Math Applications in Computer Science
  • Algebraic Topology
  • Mathematical Logic and Formal Languages
  • Complexity
  • Computation by Abstract Devices
  • Mathematical Applications in Computer Science
Label
Directed algebraic topology and concurrency, Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-15398-8
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
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 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
  • 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 Prod-Simplicial Complex; 8 Perspectives; References; Index
Dimensions
unknown
Extent
1 online resource (xi, 167 pages)
File format
unknown
Form of item
online
Isbn
9783319153988
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-15398-8
Other physical details
illustration
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)944178213
  • (OCoLC)ocn944178213
Label
Directed algebraic topology and concurrency, Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-15398-8
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
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 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
  • 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 Prod-Simplicial Complex; 8 Perspectives; References; Index
Dimensions
unknown
Extent
1 online resource (xi, 167 pages)
File format
unknown
Form of item
online
Isbn
9783319153988
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-15398-8
Other physical details
illustration
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)944178213
  • (OCoLC)ocn944178213

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