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.
This work has been supported by a Conacyt-NSF grant.
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Herlihy, M., Rajsbaum, S. (1998). A wait-free classification of loop agreement tasks. In: Kutten, S. (eds) Distributed Computing. DISC 1998. Lecture Notes in Computer Science, vol 1499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056482
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