 
Summary: On the MutualExclusion Problema
quest for minimal solutions.
Uri Abraham and Menachem Magidor
Department of mathematics and computer science
BenGurion University, Be'er Sheva, Israel;
Institute of mathematics
The Hebrew University, Jerusalem, Israel.
November 25, 1999
Abstract
We prove that there is no solution with regular registers to the
criticalsection 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.
1 Preface
The criticalsection problem posed by Dijkstra [1965] 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 mutualexclusion and lockoutfreedom? Mutualexclusion
