Summary: On the Mutual-Exclusion Problem|a
quest for minimal solutions.
Uri Abraham and Menachem Magidor
Department of mathematics and computer science
Ben-Gurion University, Be'er Sheva, Israel;
Institute of mathematics
The Hebrew University, Jerusalem, Israel.
November 25, 1999
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.
The critical-section problem posed by Dijkstra  is the following: Sup-
pose two independent processes that from time to time need to access a
common resource (like a printer); how can they coordinate the use of this re-
source and achieve mutual-exclusion and lockout-freedom? Mutual-exclusion