A New Approach for Active Automata Learning Based on Apartness

Abstract: We present $L^{#}$, a new and simple approach to active automata learning. Instead of focusing on equivalence of observations, like the $L^{\ast}$ algorithm and its descendants, $L^{#}$ takes a different perspective: it tries to establish apartness, a constructive form of inequality. $L^{#}$ does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. $L^{#}$ 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 $L^{#}$ in practice. Experiments with a prototype implementation, written in Rust, suggest that $L^{#}$ is competitive with existing algorithms.