Directed algebraic topology and concurrency. (2016)

• Record Type: Book
• Further Information: Note: Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, Martin Raussen.
• Authors: Fajstrup, Lisbeth; Goubault, Eric; Haucourt, Emmanuel; Mimram, Samuel, 1983-; Raussen, Martin, 1954-
• 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.
• Publisher Details: Cham : Springer
• Publication Date: 2016
• Extent: 1 online resource (xi, 167 pages), illustration
• Subjects: 004.01/51; Computer science; Computer multitasking -- Mathematics; Algebraic topology; COMPUTERS -- Computer Literacy; COMPUTERS -- Computer Science; COMPUTERS -- Data Processing; COMPUTERS -- Hardware -- General; COMPUTERS -- Information Technology; COMPUTERS -- Machine Theory; COMPUTERS -- Reference; 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; Mathematics -- Topology; Mathematics -- Logic; Technology & Engineering -- General; Computers -- Machine Theory; Mathematics -- Applied; Algebraic topology; Mathematical theory of computation; Cybernetics & systems theory; User interface design & usability; Mathematical modelling; Engineering; Maths for computer scientists; Electronic books
• Languages: English
• ISBNs: 9783319153988; 3319153986
• Related ISBNs: 3319153978; 9783319153971
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed March 9, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.