Abstract

Given a language generated by an automaton over an alphabet of real (or complex) numbers, and a real or complex number beta in the open unit disk, we consider the beta-direct valuation and reversed valuation sets of this language. For the k-Pell, k-Fibonacci and k-metallic languages, we compute and describe the topological properties of these valuation sets when beta is the smaller root of the polynomial associated with these languages. Furthermore, we introduce the connectivity locus for the valuations of these languages, establish bounds for these sets, and exhibit some points in their boundary