An approach to innocent strategies as graphs

International audienceThis paper proposes an approach for extending to graphs the close relation between proofs and innocent strategies. We work in the setting of L-nets, introduced by Faggian and Maurel as a game model of concurrent interaction. We show how L-nets satisfying an additional condition, which we call LS-nets, can be sequentialized into traditional tree-like strategies. Conversely, sequential strategies can be relaxed into more asynchronous ones. We develop an algebra of constructors and destructors that serve to build and decompose graph strategies, and to describe a class of minimally sequential graph strategies, which can be seen as an abstract kind of multiplicative-additive proof-nets