A wait-free classification of loop agreement tasks

Abstract

Loop agreement is a family of wait-free tasks that includes set agreement and approximate agreement tasks. This paper presents a complete classification of loop agreement tasks. Each loop agreement task can be assigned an algebraic signature consisting of a finitely-presented group G and a distinguished element g in G. This signature completely characterizes the task's computational power. If G and H are loop agreement tasks with respective signatures 〈G, g〉 and 〈H, h〉, then G implements H if and only if there exists a group homomorphism φ : G → H carrying g to h.