On the Mutual-Exclusion Problem|a quest for minimal solutions.

We prove that there is no solution with regular registers to the critical-section problem for n processes whose registers are of total size 3n 1. For n = 2 this is the best result since for total size six, solutions exist, and are presented here. We emphasize that if one of the two processes never sleeps, then solutions for two processes with regular registers of total size ve do exist