Abstract
This article intends to provide some new insights into concurrency using ideas from the theory of dynamical systems. Inherently discrete concurrency corresponds to a parallel continuous concept: a discrete state space corresponds to a differential manifold, an execution path corresponds to a flow line of a dynamical system. To model non-determinacy within dynamical systems, we introduce a new geometrical object, a section cone. A section cone is a convex set in the space of vector fields, all elements having the same singular points. We show that it is enough to consider flow lines of a single vector field in order to capture the behavior of all flow lines in the section cone up to homotopy (corresponding to equivalence of executions).
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Wisniewski, R., Raussen, M. Geometric analysis of nondeterminacy in dynamical systems. Acta Informatica 43, 501–519 (2007). https://doi.org/10.1007/s00236-006-0037-5
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DOI: https://doi.org/10.1007/s00236-006-0037-5