Brief Announcement: Stranger-Free Tasks

Delporte-Gallet et al. show that, in a system of n processes, it is both necessary and sufficient to use n multi-writer multi-reader (MWMR) registers, that are not pre-allocated, to emulate with non-blocking progress n single-writer multi-reader (SWMR) registers that are uniquely pre-allocated. They conclude with the significant result that n MWMR registers are sufficient to solve any task solvable read-write wait-free. However, they mistakenly claim - likely inadvertently - that n MWMR registers are also necessary to solve any task solvable read-write wait-free (a counterexample is the splitter task, which is solvable for any number of processes with just 2 MWMR registers).We propose the new notion of stranger-free task where, roughly speaking, for every two processes, at least one must know about the other. We show that n MWMR registers are necessary to solve stranger-free tasks. However, there is an infinite hierarchy of tasks that are not stranger-free: for every integer k > 0, we exhibit a task that is solvable for an infinite number of processes using k + 1 MWMR registers but that is not solvable for k + 1 processes using k MWMR registers. It remains an open question whether there are tasks that are not stranger-free and yet their wait-free solution requires n MWMR registers.