Polynomial Distinguishability of Timed Automata

We study the complexity of identifying (learning) timed automata in the limit from data. Timed automata are finite state models that model time explicitly, i.e., using numbers. Because timed automata use numbers to represent time, they can be exponentially more compact than models that model time implicitly, i.e., using states. We show three results that are essential in order to exactly determine when timed automata are efficiently identifiable in the limit. First, we show that polynomial distinguishability is a necessary condition for efficient identifiability in the limit. Second, we prove that deterministic time automata with two or more clocks are not polynomially distinguishable. As a consequence, they are not efficiently identifiable. Last but not least, we prove that deterministic timed automata with one clock are polynomially distinguishable, which makes them very likely to be efficiently identifiable in the limit.