We present an algorithm to learn a deterministic timed automaton (DTA) via
membership and equivalence queries. Our algorithm is an extension of the L*
algorithm with a Myhill-Nerode style characterization of recognizable timed
languages, which is the class of timed languages recognizable by DTAs. We first
characterize the recognizable timed languages with a Nerode-style congruence.
Using it, we give an algorithm with a smart teacher answering symbolic
membership queries in addition to membership and equivalence queries. With a
symbolic membership query, one can ask the membership of a certain set of timed
words at one time. We prove that for any recognizable timed language, our
learning algorithm returns a DTA recognizing it. We show how to answer a
symbolic membership query with finitely many membership queries. We also show
that our learning algorithm requires a polynomial number of queries with a
smart teacher and an exponential number of queries with a normal teacher. We
applied our algorithm to various benchmarks and confirmed its effectiveness
with a normal teacher