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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.
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.
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