A New Approach for Active Automata Learning Based on Apartness

We present $$L^{\#}$$ L # , a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the $$L^{*}$$ L ∗ algorithm and its descendants, $$L^{\#}$$ L # takes a different perspective: it tries to establish apartness, a constructive form of inequality. $$L^{\#}$$ L # does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. $$L^{\#}$$ L # has the same asymptotic query and symbol complexities as the best existing learning algorithms, but we show that adaptive distinguishing sequences can be naturally integrated to boost the performance of $$L^{\#}$$ L # in practice. Experiments with a prototype implementation, written in Rust, suggest that $$L^{\#}$$ L # is competitive with existing algorithms.