Learning reversible languages with terminal distinguishability

k-reversible languages are regular ones that offer interesting properties under the point of view of identification of formal languages in the limit. Different methods have been proposed to identify k-reversible languages in the limit from positive samples. Non-regular language classes have been reduced to regular reversible languages in order to solve their associated learning problems. In this work, we present a hierarchy of reversible languages which can be characterized by some properties related to the set of terminal segments of the automata (terminal distinguishability). Terminal distinguishability is a property that has been previously used to characterize other language families which can be identified in the limit from positive data. In the present work we combine reversibility and terminal distinguishability in order to define a new hierarchy of regular languages which is highly related to the k-reversible hierarchy. We will provide an efficient method to identify any given language in the hierarchy from only positive examples.