Stochastic Minority on Graphs

Abstract. Cellular automata have been mainly studied for on very regular graphs carrying the cells (like lines or grids) and under synchronous dynamics (all cells update simultaneously). In this paper, we study how the asynchronism and the topology of cells act upon the dynamics of the classical rule Minority. Minority has been well-studied for synchronous updates. Yet, beyond its apparent simplicity, this rule yields complex behaviors when introducing some asynchronism. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asynchronism (only one random cell updates at each time step) for several types of graphs. Such a comparitive study is a first step in understanding how the fully asynchronous dynamics is linked to the topology of the cells.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Jean-Baptiste Rouquier, Damien Regnault, Eric Thierry
• Keywords: Cellular Automata, Classical Rule Minority, CORR 2010, Education, Synchronous Dynamics