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An automata network (AN) is a finite graph where each node holds a state froma finite alphabet and is equipped with a local map defining the evolution ofthe state of the node depending on its neighbors. The global dynamics of thenetwork is then induced by an update scheme describing which nodes are updatedat each time step. We study how update schemes can compensate the limitationscoming from symmetric local interactions. Our approach is based on intrinsicsimulations and universality and we study both dynamical and computationalcomplexity. By considering several families of concrete symmetric AN underseveral different update schemes, we explore the edge of universality in thistwo-dimensional landscape. On the way, we develop a proof technique based on anoperation of glueing of networks, which allows to produce complex orbits inlarge networks from compatible pseudo-orbits in small networks.

On Symmetry versus Asynchronism: at the Edge of Universality in Automata Networks