ON THE ROOT OF LANGUAGES

In this work we study the problem of determining an unambiguous p-root of a language, i.e. a solution of the equation X^p=L when L is a language and the product is unambiguous. We show that every language admits at most one unambiguous root and that the problem of the existence of the unambiguous root is undecidable for the class of context free languages. We also prove that it is decidable whether a regular language admits a regular unambiguous root and that if a language is in P and admits the unambiguous root, then the root is in P.