On the mutual-exclusion problem - a quest for minimal solutions

Abraham, U. and M. Magidor, On the mutual-exclusion problem - a quest for minimal solutions, Theoretical Computer Science 129 (1994) 1-38. We investigate here the question of finding the minimal requirements for the registers used by n processes that solve the critical-section problem. For two processes, we show that there cannot be a solution to the critical-section problem if the two registers used are regular and of size 2 and 3. For n processes, this result generalizes to show the impossibility of a solution with regular registers if the total size of the registers is 3n - 1. This is the best result for n = 2 since there are solution (presented here) in which regular registers of total size 6 are used. The impossibility proof depends on a careful analysis of infinite protocol automata, and therefore a detailed definition of such automata and their semantics is developed first.