Directed Algebraic Topology and Concurrency
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.
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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. As a result, tools and concepts from topology have to be extended to take privileged directions into account. Accedi Cerca ordine.
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Eric Goubault 1, 2 Details. Eric Goubault 1, 2 AuthorId : Author.
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Hide details. Abstract : We show in this article that some concepts from homotopy theory, in algebraic topology, are relevant for studying concurrent programs.
We show some of the essential differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set.
Directed Algebraic Topology Concurrency by Lisbeth Fajstrup
Finally we apply some of these concepts to the proof of the safeness of a two-phase protocol, well-known and used in concurrent database theory. We end up with a list of problems from both a mathematical and a computer-scientific point of view.
Document type : Journal articles.