Petri Nets Representing the Evolution of Elementary Cellular Automata

Abstract

A Petri net (PN) is a directed graph which consists of two kinds of nodes called places and transitions. Besides their graphical representation, PN possess a mathematical formalism based on the incidence matrix and the state equation. In this paper we show that PN can be used as a general tool to represent the evolution of any elementary cellular automaton (ECA). This is performed by matrix operations obtained from the state equation of the PN which represent the cellular automaton and the use of a logical operator. It is presented an algorithm to construct a PN for any ECA and we give some comparative examples between the evolution of markings of the PN and the evolution of the respective ECA.