The Relative Power of Composite Loop Agreement Tasks

Authors Vikram Saraph, Maurice Herlihy



PDF
Thumbnail PDF

File

LIPIcs.OPODIS.2015.13.pdf
  • Filesize: 0.55 MB
  • 16 pages

Document Identifiers

Author Details

Vikram Saraph
Maurice Herlihy

Cite AsGet BibTex

Vikram Saraph and Maurice Herlihy. The Relative Power of Composite Loop Agreement Tasks. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.OPODIS.2015.13

Abstract

Loop agreement is a family of distributed tasks that includes set agreement and simplex agreement, and was used to prove the undecidability of wait-free solvability of distributed tasks by read/write memory. Herlihy and Rajsbaum defined the algebraic signature of a loop agreement task, which consists of a group and a distinguished element. They used the algebraic signature to characterize the relative power of loop agreement tasks. In particular, they showed that one task implements another exactly when there is a homomorphism between their respective signatures sending one loop to the other. In this paper, we extend the previous result by defining the composition of multiple loop agreement tasks to create a new one with the same combined power. We generalize the original algebraic characterization for relative power to compositions of tasks. In this way, we can think of loop agreement tasks in terms of their basic building blocks. We also investigate a category-theoretic perspective of loop agreement by defining a category of loops, showing that the algebraic signature is a functor, and proving that our definition of task composition is the "correct" one, in a categorical sense.
Keywords
  • Distributed computing
  • loop agreement
  • task composition
  • topology

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail