A Myhill-Nerode Characterization and Active Learning for One-Clock Timed Automata
This work addresses the long-standing absence of a Myhill–Nerode-style characterization for languages recognized by single-clock deterministic timed automata (1-DTA), a gap that has impeded the construction of canonical forms and the development of active learning algorithms. By introducing the notion of *semi-integer timed words* and their reset behaviors, the paper establishes a Myhill–Nerode-type equivalence relation tailored to 1-DTA, effectively resolving the non-canonicity issues arising from divergent clock-reset strategies along different paths. Building on this characterization, the authors devise an L*-style active learning algorithm capable of correctly inferring a canonical representation of a 1-DTA. This contribution provides the first theoretically grounded framework for the formal learnability of 1-DTA and yields the first active learning method with correctness guarantees for this class of timed systems.