On a Variant of a Method of Berstel’s and Nielsen’s

Abstract

An analogy to a result of J. Berstel’s and M. Nielsen’s, showing how equality of coefficient sets of certain N-rational sequences (DOL growth sequences) manifests itself by forcing equal periodical subsequences, is obtained for sequences of words. As applications, certain decidability problems for $\mathcal{L}$ languages are reduced to the equivalence problem for HDOL sequences.