Computing in the Presence of Concurrent Solo Executions

In a wait-free model any number of processes may crash. A process runs solo when it computes its local output without receiving any information from other processes, either because they crashed or they are too slow. While in wait-free shared-memory models at most one process may run solo in an execution, any number of processes may have to run solo in an asynchronous wait-free message-passing model. This paper is on the computability power of models in which several processes may concurrently run solo. It first introduces a family of round-based wait-free models, called the d-solo models, 1 ≤ d ≤ n, where up to d processes may run solo. The paper gives then a characterization of the colorless tasks that can be solved in each d-solo model. It also introduces the (d, ǫ)-solo approximate agreement task, which generalizes ǫ-approximate agreement, and proves that (d, ǫ)-solo approximate agreement can be solved in the d-solo model, but cannot be solved in the (d + 1)-solo model. The paper studies also the relation linking d-set agreement and (d, ǫ)-solo approximate agreement in asynchronous wait-free message-passing systems. These results establish for the first time a hierarchy of wait-free models that, while weaker than the basic read/write model, are nevertheless strong enough to solve non-trivial tasks.Dans un modèle wait-free, un nombre quelconque de processus peut arrêter de fonctionner. Un processus s'exécute en solo lorsqu'il calcule sa sortie sans communiquer avec les autres processus. Dans les modèles wait-free avec des processus communicant par mémoire partagée, au plus un processus peut s'exécuter en solo, alors que, dans les modèles wait-free ou ils échangent des messages, un nombre quelconque d'entre eux peut avoir à s'exécuter en solo. Cet article étudie la calculabilité dans des modèles intermédiaires, appelés d-solo modèles, dans lesquels au plus d processus s'exécutent en solo