Concurrency in Interaction Nets and Graph Rewriting

In this work, we study concurrency in non-deterministic extensions of Lafont's interaction nets (a graphical language for functional calculus). These extensions are essentially of three types: multiruled, with multiports and multiwired. They can be combined creating thus seven types of concurrent interaction nets. A first task is to determine a good structural operational semantics to be able to compare the behaviors of these extensions. Based on a known technique in graph rewriting - double pushout with borrowed contexts - we define a method of labeling transitions using derivation rules in the style of process calculi, usual paradigm for modeling concurrency. Moreover, we define an observational semantics based on a parametric notion of barbs, that allows us to give a precise notion of translation between systems. We consider an extensions is more expressive than another if all languages from the second one can be translated into a language of the first one. This allows us to classify the concurrent interaction nets systems into three layers. From the strongest to the weakest: nets with multiport cells, nets with multiwires and finally multiruled nets. Using this, we build a universal language for concurrent interaction nets, which study enlightens us on the fundamental bricks of concurrency.