Séminaire général du Département d’informatique
< précédent | suivant >
|Un survol sur la topologie algébrique dirigée : des applications à la théorie de la concurrence|
Éric Goubault (CEA LIST)
16 mars 2010
In the early 90s, quite independently, a number of computer-scientific problems appeared to introduce algebraic topological techniques. These include truly-concurrent semantics for concurrency, fault-tolerant protocols for distributed systems, rewriting systems theory… Since then, two major phenomena arose: the apparition of new homotopical/homological theories motivated by applications, in particular "directed topology" in concurrency applications, and the view that topological invariants computations are amenable to "numerical schemes" like approximations (this is now called "applied algebraic topology", and has deep developments in robotics, and in computational geometry). Now, it is reasonable to think that, although most of the development in the field of directed algebraic topology was foundational and almost purely mathematical during 15 years or so, applications to real-size problems in static analysis of concurrent systems, for instance, are now possible. We will present in this talk some of the major concepts of directed algebraic topology, its historical ramifications (both in applications and theory) and some current applications to state-space reduction in semantics/analysis of concurrent systems.