In this article, written jointly with Enrico Formenti and Bruno Durand, we present a new approach to cellular automata (CA) classification based on algorithmic complexity. We construct a parameter κ which is based only on the transition table of CA and measures the "randomness" of evolutions; κ is better, in a certain sense, than any other parameter recursively definable on CA tables. We investigate the relations between the classical topological approach and ours one. Our parameter is compared with Langton's λ parameter: κ turns out to be theoretically better and also agrees with some practical evidences reported in literature. Finally, we propose a protocol to approximate κ and make experiments on CA dynamical behavior.

We explain the basics of the theory of the Kolmogorov complexity, also known as algorithmic information theory, and underline the main differences between the Kolmogorov complexity and Kolmogorov prefix complexity. Then, we introduce the definition of randomness for either finite or infinite words according to Per Martin-Löf and show that it is equivalent to the notion of uncompressibility defined via Kolmogorov complexity.