Irreducible ambiguities in monoids of words

The starting point of this study is that the written form of certain South-East Asian languages does not use spaces between words, thus complicating their automatic processing. This is particularly the case on the syllabic level, where generally the text cannot be cut up uniquely. From the formal combinatorics point of view, the syllabic system of these languages is not a code. We will focus on the origin of the splitting ambiguities, more specifically on the inventory of the so-called irreducible ambiguities, in the sense that all others originate from them. We prove that the language of irreducible ambiguities is rational. Then we present a method to compute one of its regular expressions, illustrating the method with the experience of its application to the Lao language.