  Modules were introduced as an extension of Boolean automata networks. They
have inputs which are used in the computation said modules perform, and can be
used to wire modules with each other. In the present paper we extend this new
formalism and study the specific case of acyclic modules. These modules prove
to be well described in their limit behavior by functions called output
functions. We provide other results that offer an upper bound on the number of
attractors in an acyclic module when wired recursively into an automata
network, alongside a diversity of complexity results around the difficulty of
deciding the existence of cycles depending on the number of inputs and the size
of said cycle.
