Bigger is Not Always Better: on the Quality of Hypotheses in Active Automata Learning

In Angluin’s L∗ algorithm a learner constructs a sequence of hypotheses in order to learn a regular language. Each hypothesis is consistent with a larger set of observations and is described by a bigger model. From a behavioral perspective, however, a hypothesis is not always better than the previous one, in the sense that the minimal length of a counterexample that distinguishes a hypothesis from the target language may decrease. We present a simple modification of the L∗ algorithm that ensures that for subsequent hypotheses the minimal length of a counterexample never decreases, which implies that the distance to the target language never increases in a corresponding ultrametric. Preliminary experimental evidence suggests that our algorithm speeds up learning in practical applications by reducing the number of equivalence queries.