On asymmetric progress conditions

Wait-freedom and obstruction-freedom have received a lot of attention in the literature. These are symmetric progress conditions in the sense that they consider all processes as being "equal". Wait-freedom has allowed to rank the synchronization power of objects in presence of process failures, while (the weaker) obstruction-freedom allows for simpler and more efficient object implementations. This paper introduces the notion of asymmetric progress conditions. Given an object O in a shared memory system of n processes, we say that O satisfies (y, x)-liveness if O can be accessed by a subset of y ≤ n processes only, and it guarantees wait-freedom for x processes and obstruction-freedom for the remaining y-x processes. Notice that, (n, n)-liveness is wait-freedom while (n, 0)-liveness is obstruction-freedom. The main contributions are: (1) an impossibility result showing that there is no (n, 1)-live consensus object even if one can use underlying (n- 1, n-1)-live consensus objects and registers, (2) an (n, x)-liveness hierarchy for 0 ≤ x ≤ n, and (3) an impossibility result showing that there is no consensus object for n processes that is obstruction-free with respect to all processes and fault-free with respect to a single process even if one can use underlying (n - 1, n - 1)-live consensus objects and registers (a process is fault-free if it always terminates when all the processes participate and there are no faults). (4) An implementation based on (x, x)-live objects that constructs a consensus object for any number of n ≥ x processes which satisfies an asymmetric group-based progress condition.