Prime Numbers as a Tool to Design Distributed Algorithms

Abstract Prime numbers are investigated as a tool to design distributed control algorithms. One of the major drawbacks in designing such algorithms lies in the inability for one or several processes (or even for an external observer) to catch instantaneously some part of the global state of the system. It is shown in this paper how, in some cases, prime numbers can be used to make distributed observations allowing to make consistent decisions. Two very different distributed algorithms are produced as an illustration of the proposed tool (a mutual exclusion and a termination detection algorithm).