C'est maintenant
Le 2017-05-17 14:56, breuvart a écrit :
> Le séminaire d'équipe LCR du LIPN de ce vendredi (ci-dessous) pourra
> potentiellement intéresser au delà. Toute participation extérieure est
> la bienvenue.
>
>
> Directed homology theories for geometric models of true concurrency
>
> Jérémy Dubut, LSV (ENS Cachan)
>
> Salle B107, bâtiment B, Université de Villetaneuse
>
> 19/05/2017 11:00 - 12:30
>
> Résumé :
>
> Studying a system through its geometry is the main purpose of directed
> algebraic topology. This topic emerged in computer science, more
> particularly in true concurrency, where Pratt introduced his higher
> dimensional automata (HDA) in 1991 (actually, the idea of geometry of
> concurrency can be tracked down Dijkstra in 1965). Those automata are
> geometric by nature: every set of n processes executing independent
> actions can be modeled by a n-cube, and such an automata then gives
> rise to a topological space, obtained by glueing such cubes together,
> with a specific direction of time coming from the execution flow. It
> then seems natural to use tools from algebraic topology to study those
> spaces: paths model executions, homotopies of paths, that is
> continuous deformations of paths, model equivalence of executions
> modulo scheduling of independent actions, and so on, but all those
> notions must preserve the direction somehow. This brings many
> complications and the theory must be done again, essentially from
> scratch.
>
> In this talk, after developing this idea of geometry of true
> concurrency, I will focus on homology. Homology is a nice computable
> tool from algebraic topology and it is a challenge in directed
> algebraic topology to find a satisfactory analogue that behaves well
> with direction. I will present our candidate of `directed homology’,
> called natural (or bimodule) homology. This object consists in a
> functor with values in modules, which looks at the classical homology
> of trace spaces (a nice abstraction of what we may call `space of
> executions’) and how those homologies evolve with time. This evolution
> can be studied through an abstract notion of bisimulation of functors
> with values in modules, that has many equivalent characterizations
> (using relations, using lifting properties, using Grothendieck
> construction, …) and whose existence is decidable in simple cases.
> Finally, among nice properties of our directed homology, I will show
> you that it is computable on simple spaces, which are already enough
> to model simple truly concurrent systems.
>
> Joint work with Eric Goubault and Jean Goubault-Larrecq.
