Automatic group

rdf:langString Automatic group

rdf:langString In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a "canonical form" and can tell if two elements given in canonical words differ by a generator. More precisely, let G be a group and A be a finite set of generators. Then an automatic structure of G with respect to A is a set of finite-state automata: * the word-acceptor, which accepts for every element of G at least one word in representing it; * multipliers, one for each , which accept a pair (w1, w2), for words wi accepted by the word-acceptor, precisely when in G. The property of being automatic does not depend on the set of generators.