TY - BOOK AU - Fajstrup,Lisbeth AU - Goubault,Eric AU - Haucourt,Emmanuel AU - Mimram,Samuel AU - Raussen,Martin ED - SpringerLink (Online service) TI - Directed Algebraic Topology and Concurrency SN - 9783319153988 AV - QA76.9.M35 U1 - 004.0151 23 PY - 2016/// CY - Cham PB - Springer International Publishing, Imprint: Springer KW - Computer science KW - Computers KW - Mathematical logic KW - Mathematics KW - Computer mathematics KW - Algebraic topology KW - Complexity, Computational KW - Computer Science KW - Math Applications in Computer Science KW - Algebraic Topology KW - Mathematical Logic and Formal Languages KW - Complexity KW - Computation by Abstract Devices KW - Mathematical Applications in Computer Science N1 - 1 Introduction -- 2 A toy language for concurrency -- 3 Truly concurrent models of programs with resources -- 4 Directed topological models of concurrency -- 5 Algorithmics on directed spaces.\\ N2 - 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 UR - http://148.231.10.114:2048/login?url=http://dx.doi.org/10.1007/978-3-319-15398-8 ER -