7 avril 2025
Pierre-Yves Coursolle (LACL)For the analysis of concurrent programs, higher-dimensional automata (HDA) are models that help to limit the combinatorial explosion that can be observed with interleaving models. Such an automaton has a fundamentally geometric interpretation: it can be seen as a construction plan indicating how to glue together elementary topological spaces such as segments, squares, cubes, etc. In order to retrieve the semantics of the program in the topological space previously constructed, the latter must have a notion of local direction. To axiomatize this idea of local direction, several non-equivalent approaches have been proposed in the literature, such as d-spaces, streams, locally ordered spaces and so on.
In this talk, we present a unified framework, inspired by topological spaces, which can contain and compare these different approaches, and, more generally, in which it is possible to define all kinds of locally structured spaces. We show that many topological notions generalize to this framework, and that streams have a natural place in it.