Some Invariants of Directed Topology towards a Theoretical Base for a Static Analyzer Dealing with Fine-Grain Concurrency

We define the geometric models of conservative programs. Those models belong to a class of objects, the isothetic regions, that is contained in most of the categories introduced as framework for directed topology. We describe some invariants of directed topology and prove that they are well-behaved for isothetic regions. In particular, the class of isothetic regions satisfy a unique decomposition property that is related to parallelization of programs.

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