Circuit metaconstruction in logspace for Rice-like complexity lower bounds in ANs and SGRs

A new proof technique combining finite model theory and dynamical systems has recently been introduced to obtain general complexity lower bounds on any question one may formulate on the dynamics (seen as a graph) of a given automata network (AN). ANs are abstract finite dynamical systems of interacting entities whose evolution rules are encoded as circuits, hence the study also applies to succinct graph representations (SGRs). In this article, we detail the construction of circuits to obtain general complexity lower bounds (metareduction) and show that the reduction is feasible in logarithmic space.