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A Semigroup Approach to Automaticity
Andreas W.M. Dress1 and F.von Haeseler2
1Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany
dress@mathematik.uni-bielefeld.de
2ESAT/SISTA KU-Leuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium
friedrich.vonhaeseler@esat.kuleuven.ac.be
Annals of Combinatorics 7 (2) p.171-190 June, 2003
AMS Subject Classification: 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 or 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 . We show that the main results characterizing automatic sequences (Cobham, 1972, Math. Systems Theory 6) hold almost verbatim in the general context, too.
Keywords: automatic sequences, finite automata, semigroup actions, categories

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