Learning Omega-Regular Languages: A Tour of Learning Results and Canonical Representations

Learning regular languages of finite words is guided by the Myhill–Nerode congruence and the minimal DFA. For ω-regular languages, the picture is more fragmented: different learning results rely on different representations, each with its own algorithmic and succinctness properties. This survey presents the main paradigms and results for learning ω-regular languages, including passive learning, active query learning, polynomial predictability, characteristic samples, and efficient teachability. We cover negative results for nondeterministic ω-automata, positive results for informative and weak classes, learning through FDFAs, SUBAs and M2MAs, and recent canonical models based on history determinism and natural colors. Throughout, we emphasize that learnability guarantees must be understood together with the succinctness of the target representation.