  We propose a query learning algorithm for residual symbolic finite automata
(RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions
are labeled by predicates over a Boolean algebra, in which a big collection of
characters leading the same transition may be represented by a single
predicate. Residual finite automata (RFAs) are a special type of
non-deterministic finite automata which can be exponentially smaller than the
minimum deterministic finite automata and have a favorable property for
learning algorithms. RSFAs have both properties of SFAs and RFAs and can have
more succinct representation of transitions and fewer states than RFAs and
deterministic SFAs accepting the same language. The implementation of our
algorithm efficiently learns RSFAs over a huge alphabet and outperforms an
existing learning algorithm for deterministic SFAs. The result also shows that
the benefit of non-determinism in efficiency is even larger in learning SFAs
than non-symbolic automata.
