The following technical report is available from http://aib.informatik.rwth-aachen.de:

Learning Visibly One-Counter Automata in Polynomial Time Daniel Neider, Christof Löding AIB 2010-02

Visibly one-counter automata are a restricted kind of one-counter automata: The input symbols are typed such that the type determines the instruction that is executed on the counter when the input symbol is read. We present an Angluin-like algorithm for actively learning visibly one-counter automata that runs in polynomial time in characteristic parameters of the target language and in the size of the information provided by the teacher.