A group is stackable if there is a discrete dynamical system on its Cayley graph that flows edges towards a set spanning tree. The group is autostackable if this flow is computable by a finite state automaton (FSA). In this talk we will introduce autostackability, give examples of autostackable groups, and show that the fundamental group of every closed 3--manifold is autostackable. This provides a common algorithm to solve the word problem for such groups using only FSAs, realizing a goal of Epstein et. al. This is joint work with Mark Brittenham and Susan Hermiller.