Identifying regular languages over partially commutative monoids

We define a new technique useful in identifying a subclass of regular languages defined on a free partially commutative monoid (regular trace languages), using equivalence and membership queries. Our algorithm extends an algorithm defined by Dana Angluin in 1987 to learn DFA's. The words of a trace language can be seen as equivalence classes of strings. We show how to extract, from a given equivalence class, a string of an unknown underlying regular language. These strings can drive the original" learning algorithm which identify a regular string language that defines also the target trace language. In this way the algorithm applies also to classes of unrecognizable regular trace languages and, as a corollary, to a class of unrecognizable string languages. We also discuss bounds on the number of examples needed to identify the target language and on the time required to process them.