Active Automata Learning: from L* to L#

In this tutorial on active automata learning algorithms, I will start with the famous L
^*
algorithm proposed by Dana Angluin in 1987, and explain how this algorithm approximates the Nerode congruence by means of refinement. Next, I will present a brief overview of the various improvements of the L
^*
algorithm that have been proposed over the years. Finally, I will introduce L
^#
, a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the L
^*
algorithm and its descendants, L
^#
takes a different perspective: it tries to establish apartness, a constructive form of inequality.