International audienceA Petri net is reversible if its initial marking is a home marking, a marking reachable from any reachable marking. This property is fundamental in man-made systems as it lets a system return to its initial state using only internal operations.Necessary and sufficient conditions are already known for the reversibility of well-formed Choice-Free and ordinary Free-Choice nets. Like the homogeneous Join-Free nets, these nets constitute subclasses of Equal-Conflict nets. In this larger class, the reversibility property is not well understood.This paper provides the first characterization of reversibility for all the live Equal-Conflict systems by extending, in a weaker form, a known condition that applies to the Choice-Free and Free-Choice subclasses. We also show that this condition is tightly related to the Equal-Conflict class and does not apply to several other classes

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Heterogeneous computing systems became a popular and powerful platform, containing several heterogeneous computing elements (e.g. CPU+GPU). In this paper, we consider that we have two platforms, each with an unbounded number of processors. We want to execute an application represented as a Directed acyclic Graph (DAG) using these two platforms. Each task of the application has two possible execution times, depending on the platform it is executed on. Also, there is a cost to transfer data from one platform to another between successive tasks. The goal here is to minimize the finish execution time of the last task of the application (usually called makespan). We show that the problem is NP-complete for graphs of depth at least 3 but polynomial for graphs of depth at most 2. Finally, we focus on particular classes of graphs, by providing polynomial-time algorithms for bi-partite graphs, trees and 2-series-parallel graphs with different assumptions on communication delays.Résumé : Les systèmes de calculs hétérogènes (par exemple CPU+GPU) sont des plateformes populaires. Dans ce travail, nous considérons une machine avec deux plateformes homogènes de calcul, chacune contenant un nombre illimité de ressources de calcul. Nous cherchons à exécuter une application représentée par un graphe de dépendance dirigé et acyclique sur ces plateformes. Chaque tâche de l'application a deux possible modèle d'exécution en fonction de la plateforme sur laquelles elles sont exécutées. En plus nous considérons un coût de communication entre deux tâches successives si elles ne sont pas exécutées sur la même plateforme. Nous travaillons à minimiser le temps d'exécution de l'application.Nous montrons que le problème est NP-complet pour les graphes de profondeur au moins trois, mais polynomial pour les graphes de profondeur au plus deux. En plus, nous montrons qu'il est possible de calculer des solutions optimales en temps polynomial pour certaines classes de graphes définies récursivement (arbres, graphes série-parallèles).