The Expressibility of Languages and Relations by Word Equations

Classically, several properties and relations of words, such as being a power of a same word, can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain properties of words are not expressible as components of solutions of word equations. In particular, the primitiveness and the equal length are such properties, as well as being any word over a proper subalphabet.