From wait-free to arbitrary concurrent solo executions in colorless distributed computing

• Published in: Theoretical computer science Vol. 683; pp. 1 - 21
• Main Authors: Herlihy, Maurice, Rajsbaum, Sergio, Raynal, Michel, Stainer, Julien
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 30-06-2017; Elsevier
• Subjects: Approximate agreement; Asynchronous system; Colorless task; Computational Engineering, Finance, and Science; Computer Science; Read–write shared memory; Topology; Wait-free computing; Wait-free computing; Read–write shared memory; Colorless task; Asynchronous system; Topology; Approximate agreement
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2017.04.007

In an asynchronous distributed system where any number of processes may crash, a process may have to run solo, computing its local output without receiving any information from other processes. In the basic shared memory system where the processes communicate through atomic read/write registers, at most one process may run solo.
This paper introduces the family of d-solo models, where d-processes may concurrently run solo, 1≤d≤n (the 1-solo model is the basic read/write model). The paper then studies distributed colorless computations in the d-solo models, where process ids are not used, either in task specifications or during computation. It presents a characterization of the colorless tasks that can be solved in each d-solo model. Colorless tasks include consensus, set agreement and many other previously studied tasks. It shows that colorless algorithms have limited computational power for solving tasks, only when d>1. When d=1, colorless algorithms can solve the same tasks as algorithms that may use ids. It is well-known that, while consensus is not wait-free solvable in a model where at most one process may run solo, ϵ-approximate agreement is solvable. In a d-solo model, the fundamental solvable task is (d,ϵ)-solo approximate agreement, a generalization of ϵ-approximate agreement. Indeed, (d,ϵ)-solo approximate agreement can be solved in the d-solo model, but not in the (d+1)-solo model.
Finally, the paper studies a link between the solvability of d-set agreement and (d,ϵ)-solo approximate agreement in asynchronous wait-free message-passing systems, which provides an insight on the “maximal partitioning” allowed to solve an approximate agreement task.