Kolmogorov Complexity and Cellular Automata Classiication Ecole Normale Supérieure De Lyon Kolmogorov Complexity and Cellular Automata Classiication Kolmogorov Complexity and Cellular Automata Classiication

We present a new approach to cellular automata (CA for short) classiica-tion based on algorithmic complexity. We construct a parameter which is based only on the transition table of CA and measures the \randomness" of evolutions; is better, in a certain sense, than any other parameter deened on rule tables. We investigate the relations between the classical approach based on topology and ours based on algorithmic randomness. We also compare our parameter with Langton's one: we prove that ours is theoretically better and also agrees with some practical evidences reported in literature. Finally we propose a protocol to approximate and to make experiments on CA dynamical behavior. Nous pr esentons une nouvelle approche a la classiication des automates cellulaires, approche fond ee sur la complexit e algorithmique. Nous constru-isons un param etre prenant en compte la table de transitions de l'automate cellulaire consid er e. Notre th ese est que ce param etre mesure le caract ere al eatoire des evolutions de l'automate cellulaire consid er e. Nous prouvons qu'il est meilleur que tout autre param etre d eeni sur les tables de transitions. Nous nous int eressons aux liens entre notre approche et l'analyse classique qui utilise des arguments topologiques. Nous comparons aussi notre param etre a celui de Langton et prouvons non seulement que le notre est meilleur d'un point de vue th eorique mais en plus qu'il rend mieux compte de r esultats exp erimentaux qu'on peut trouver dans la litt erature. Finale-ment nous pr esentons un protocole d'exp erimentations approchant de faa con satisfaisante notre param etre. Abstract We present a new approach to cellular automata (CA for short) classiication based on algorithmic complexity. We construct a parameter which is based only on the transition table of CA and measures the \randomness" of evolutions; is better, in a certain sense, than any other parameter deened on rule tables. We investigate the relations between the classical approach based on topology and ours based on algorithmic randomness. We also compare our parameter with Lang-ton's one: we prove that ours is theoretically better and also agrees with some practical evidences reported in literature. Finally we propose a protocol to approximate and to make experiments on CA dynamical behavior.