On the existence of booster types

A data type´s consensus number measures its power in asynchronous concurrent models of computation. We characterize the circumstances under which types of high consensus number can be constructed from types with lower consensus numbers, a process called boosting. In settings where boosting is impossible, we can reason about the synchronization power of objects in isolation. We give a new and simple topological condition, called κ-solo-connectivity sufficient to ensure that one-shot types cannot be boosted to consensus number κ. The booster type need not be one-shot; it can be arbitrary. We also show that, for κ>2, any type that is not κ-solo-connected can be boosted to consensus number κ. For types that can be boosted, we establish an upper bound on the amount the consensus number can be increased. For finite types, these properties and bounds are computable. For deterministic one-shot types, the κ-solo-connectivity property also exactly characterizes the types that have consensus number less than κ