A Morphic Representation of Complements of Recursively Enumerable Sets

After extending two word morphismsfand g to languages, an equationf(X) = g(X) can be written and ItS language soluUons investigated. An elementary characterization of the famdy of all solutions of the equation is ~ven, and it is used to mvesttgate the maximal solution which is the mum subject of this paper. It turns out that going through all propagating morphismsf and g, the family of maximal solutions obtained equals the famdy of complements of recurslvely enumerable languages after intersecting with regular languages and mapping with propagating morphisms. In the general case (of arbitrary morphismsf and g) the corresponding family is larger and includes the full-AFL closure of the family of complements of recursively enumerable languages.