Abstract
In this paper, a system of anonymous processes is considered that communicates with beeps through multiple channels in a synchronous communication model. In beeping channels, processes are limited to hearing either a beep or a silence from the channel with no collision detection. A strong model is assumed in which a process can beep on any single channel and listen on any specific channel during a single round. The goal is to develop distributed naming algorithms for two models where the number of processes is either known or unknown. A Las Vegas algorithm was developed for naming anonymous processes when the number of processes is known. This algorithm has an optimal time complexity of O(n log n) rounds and uses O(n log n) random bits, where n is the number of processes for the largest group. For the model with an unknown number of processes, a Monte Carlo algorithm was developed, which has an optimal running time of O(n log n) rounds and a probability of success that is at least 1 - 1/2(Omega(log) (n)). The algorithms solve the naming problem in new models where processes communicate through multiple channels.