c Birkhauser Verlag, Basel, 2003 Annals of Combinatorics

AMS Subject Classication: 11B85, 68Q45, 16W22, 18DXX Abstract. We present an abstract, yet rather natural concept of automaticity which is based on semigroup actions. The standard notion of k-automaticity as well as many, if not all of its generalizations are recovered by specifying appropriate semigroup actions on N0 or NN0 or other similar objects e.g., the standard notion of k-automaticity is recovered by considering a certain natural action of the free semigroup with k generators on N0: We show that the main results characterizing automatic sequences (Cobham, 1972, Math. Systems Theory 6) hold almost ver-batim in the general context, too