Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dim ensional cellular automata (CA) is analyzed. It is shown that the transition to synchronizatio n is characterized by a dramatic increase of the statistical complexity of the patterns generated by t he difference automaton. This singular behavior is verified to be present in several CA rules display ing complex behavior. Despite all the efforts devoted to understand the meaning of complexity, we still do not have an instrument in the laboratories specially designed for quantifying this property. M aybe this is not the final objective of all those theoretical attempts carried out in the most diverse fields of know ledge in the last years [1, 2, 3, 4, 5, 6, 7, 8], but, for a moment, let us think in that possibility.