A classification of wait-free loop agreement tasks

  • Authors:

  • Maurice Herlihy;Sergio Rajsbaum

  • Affiliations:

  • Computer Science Department, Brown University, Providence, RI;Instituto de Matemáticas, U.N.A.M., Ciudad Universitaria, D.F. 04510, Mexico City, México

  • Venue:
  • Theoretical Computer Science - Special issue: Distributed computing
  • Year:
  • 2003

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Abstract

Loop agreement is a family of wait-free tasks that includes instances of set agreement and approximate agreement tasks. A task G implements task F if one can construct a solution to F from a solution to G, possibly followed by access to a read/write memory. Loop agreement tasks form a lattice under this notion of implementation.This paper presents a 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 characterizes the task's power to implement other tasks. If F and G are loop agreement tasks with respective signatures 〈F,f〉 and 〈G,g〉, then F implements G if and only if there exists a group homomorphism h : F → G carrying f to g.