On the Relation Between Chip Firing Games and Petri Nets

Abstract

We represent a new approach to investigate the famous discrete dynamical system chip firing game (CFG) by using Petri net. First, we discuss about the definition and some main results of chip firing game using different classical approaches. Then, we consider extensions of CFG, especially the class of coloured chip firing games, which corresponds to the class of lower locally distributive lattice. Our main result is to construct injections mapping each chip firing game or each coloured chip firing game to a special Petri net.