Directed Algebraic Topology and Concurrency
Directed Algebraic Topology and Concurrency
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有向代数拓扑和并发
DOI：
10.1007/978-3-319-15398-8
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Raussen
中科院分区：
文献类型：
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作者：
L. Fajstrup;É. Goubault;E. Haucourt;S. Mimram;M. Raussen
这本专著提出了一个应用的概念和方法，从代数拓扑模型的并发进程在计算机科学和他们的分析。以著名的离散模型为出发点，在资源管理的并发进程，这本书继续完善组合和拓扑模型。在这个过程中，它开发的工具和不变量的新学科的指导代数拓扑，这是由基本的研究兴趣，以及应用程序，主要是在静态分析的并发程序。并发程序的状态空间被描述为一个高维空间，其拓扑结构编码了系统的基本属性。为了分析状态空间中所有可能的执行，必须考虑的不仅仅是拓扑属性：执行路径需要遵守时间流给出的偏序。因此，必须扩展拓扑学的工具和概念，以考虑特权方向。这本书的目标读者包括研究生，研究人员和从业人员在该领域，数学家和计算机科学家一样。
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.