Greedy expansions and sets with deleted digits

We generalize a result of Daróczy and Kátai, on the characterization of univoque numbers with respect to a non-integer base (Publ. Math. Debrecen 46(3-4) (1995) 385) by relaxing the digit alphabet to a generic set of real numbers. We apply the result to derive the construction of a Büchi automaton accepting all and only the greedy sequences for a given base and digit set. In the appendix, we prove a more general version of the fact that the expansion of an element x∈Q(q) is ultimately periodic, if q is a Pisot number.