Automata networks are general models of interacting entities, exhibiting "complex" collective behaviors. Relating the local rules followed by the entities, the architecture of interactions, and the global dynamics, motivates the community. ALARICE aims at understanding these relations through the formal framework of computational complexity theory. This renewed point of view explains why some structural bounds from the literature are still loose despite considerable efforts: the inferences at stake involve algorithmically complex decisions. Our project relies on promising initial results obtained by members of the consortium, and is threefold. 1- Unveil metatheorems of the form "any non-trivial question of type X expressed in logic Y is Z-hard" for various X such as "given the local rules, question on the graph of the dynamics", Y in {FO,MSO,...} and Z in {P,NP,...}. We have a first "à la Rice" result of this flavour, presented at STACS'2021 (Y=FO, Z=NP), with a proof technique based on abstract pumping, using tools from finite model theory in order to construct (polytime) metareductions. 2- Characterize the formal complexity of new natural problems, in particular related to the network architecture. Getting a mature understanding of the constructions is a preliminary step towards metastatements. 3- Transfer this knowledge to other models of computation, via strict simulations acting as reductions. Our consortium is build around a core expertise on automata networks, complexity and simulation. It aims to enroll strong additional expertises from related fields (finite model theory, lattice dualization, graph parameterization), in order to nourish the fruitful articulations recently discovered.