A Graph Abstract Machine Describing Event Structure Composition 1

Event structures, Game Semantics strategies and Linear Logic proof-nets arise in different domains (concurrency, semantics, proof-theory) but can all be described by means of directed acyclic graphs (dag's). They are all equipped with a specific notion of composition, interaction or normalization.We report on-going work, aiming to investigate the common dynamics which seems to underly these different structures.In this paper we focus on confusion free event structures on one side, and linear strategies [Jean-Yves Girard. Locus solum. Mathematical Structures in Computer Science, 11:301–506, 2001, C. Faggian and F. Maurel. Ludics nets, a game model of concurrent interaction. In Proc. of LICS'05 (Logic in Computer Science). IEEE Computer Society Press, 2005] on the other side. We introduce an abstract machine which is based on (and generalizes) strategies interaction; it processes labelled dag's, and provides a common presentation of the composition at work in these different settings.