Directed Algebraic Topology and Concurrency

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and to their analysis. The state space of a concurrent program is described as a higher-dimensional space whose topology encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than just topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a consequence, tools and concepts from topology have to be extended to take privileged directions into account.§§With a point of departure in well-known discrete models for concurrent processes with resource management, the book develops refinements in terms of combinatorial and topological models. Along the line, it motivates and develops tools and invariants for the new discipline directed algebraic topology that is driven by fundamental research interests as well as by applications in primarily the static analysis of concurrent programs.§§The target audience for this book consists of graduate students, researchers and practitioners in the field, both mathematicians and computer scientists.§