Probabilistic pi-calculus and Event Structures

Accepté pour le workshop QAPL 2007, associé à ETAPSInternational audienceThis paper proposes two semantics of a probabilistic variant of the pi-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed pi-calculus

A graph abstract machine describing event structure composition

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 [Gir01,FM05] 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.