Representations and Complexity of Abelian Automaton Groups
Automaton groups are a class of groups generated by invertible finite-state transducers. We study representations of abelian automaton
groups and their applications to the complexity of computational problems arising within these groups. We demonstrate a correspondence
between abelian automaton groups and a class of ideals of a corresponding algebraic number field. Properties of this number field are
utilized to construct efficient algorithms for problems related to orbits of finite state transductions.