Abstract
In the wait-free shared memory model substantial attention has been devoted to understanding the relative power of sub-consensus tasks. Two important sub-consensus families of tasks have been identified: k-set agreement and M-renaming. When 2 ≤ k ≤ n − 1 and n ≤ M ≤ 2n − 2, these tasks are more powerful than read/write registers, but not strong enough to solve consensus for two processes.
This paper studies the power of renaming with respect to set agreement. It shows that, in a system of n processes, n-renaming is strictly stronger than (n − 1)-set agreement, but not stronger than (n − 2)-set agreement. Furthermore, (n + 1)-renaming cannot solve even (n − 1)-set agreement. As a consequence, there are cases where set agreement and renaming are incomparable when looking at their power to implement each other.
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Castañeda, A., Imbs, D., Rajsbaum, S., Raynal, M. (2012). Renaming Is Weaker Than Set Agreement But for Perfect Renaming: A Map of Sub-consensus Tasks. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_13
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