 
Summary: Cellular Automata equivalent to D0L Systems
Abdel Latif Abu Dalhoum, Alfonso Ortega, Manuel Alfonseca
Ingeniería Informática
Universidad Autónoma de Madrid
Campus de Cantoblanco, 28049 Madrid
Spain
{Abdel.Latif;Alfonso.Ortega; Manuel.Alfonseca }@ii.uam.es
Abstract:  This paper describes an algorithm for the construction of a certain onedimensional cellular
automaton equivalent to a given D0L system. A cellular automaton is considered equivalent to an Lsystem if
both generates the same words in the same order. Our cellular automata produce the same words and in the same
order as the given D0L system for a finite number of derivations. There is no constraint to the D0L system
considered, so the method is a general algorithm and can be used as a proof for an equivalence theorem.
KeyWords:  Cellular automata, Lindenmayer systems, parallel derivation grammar, theoretical computer
science, formal languages
1 Introduction
A D0L system [1] is a threefold with an alphabet (a
finite nonempty set of symbols); a set of production
rules that determines the only way each symbol of the
alphabet can be changed by a word; and a starting
word or axiom. A derivation of a word in a D0L
