A Myhill-Nerode Characterization and Active Learning for One-Clock Timed Automata
This work offers a foundational characterization and learning method for a specific class of timed automata, which is incremental but valuable for formal verification and synthesis communities.
The paper provides a Myhill-Nerode characterization for one-clock deterministic timed automata (1-DTA) and develops L*-style active learning algorithms for them, addressing the challenge of non-canonical resets.
We present a Myhill-Nerode style characterization for languages recognized by one-clock deterministic timed automata (1-DTA). Although there is only one clock, distinct automata may reset it differently along the same word. This adds a significant challenge in the search for a canonical automaton. Our characterization is based on a new perspective of 1-DTAs in terms of "half-integral" words that they accept, along with the reset information encoded by them. We apply our results to develop L* style algorithms that learn the canonical 1-DTA.