BERTRAND NUMERATION SYSTEMS AND RECOGNIZABILITY

There exist various well-known characterizations of sets of numbers re cognizable by a finite automaton, when they are represented in some in teger base p greater than or equal to 2. We show how to modify these c haracterizations, when integer bases p are replaced by linear numerati on systems whose characteristic polynomial is the minimal polynomial o f a Pisot number. We also prove some related interesting properties.