eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-04-06
7:1
7:15
10.4230/LIPIcs.OPODIS.2016.7
article
Set-Consensus Collections are Decidable
Delporte-Gallet, Carole
Fauconnier, Hugues
Gafni, Eli
Kuznetsov, Petr
A natural way to measure the power of a distributed-computing model is to characterize the set of tasks that can be solved in it. In general, however, the question of whether a given task can be solved in a given model is undecidable, even if we only consider the wait-free shared-memory model. In this paper, we address this question for restricted classes of models and tasks. We show that the question of whether a collection C of (l, j)-set consensus objects, for various l (the number of processes that can invoke the object) and j (the number of distinct outputs the object returns), can be used by n processes to solve wait-free k-set consensus is decidable. Moreover, we provide a simple O(n^2) decision algorithm, based on a dynamic programming solution to the Knapsack optimization problem. We then present an adaptive wait-free set-consensus algorithm that, for each set of participating processes, achieves the best level of agreement that is possible to achieve using C. Overall, this gives us a complete characterization of a read-write model defined by a collection of set-consensus objects through its set-consensus power.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol070-opodis2016/LIPIcs.OPODIS.2016.7/LIPIcs.OPODIS.2016.7.pdf
Decidability
distributed tasks
set consensus
Knapsack problem