Query Learning Algorithm for Residual Symbolic Finite Automata

Abstract

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.

Inferring Symbolic Automata

“…In particular, an extension of L * , termed MAT * , to learn SFAs was provided in [AD18] which proved that SFAs over an algebra A can be efficiently learned using MAT * if and only if the underlying algebra is efficiently learnable, and the size of disjunctions of k predicates does not grow exponentially in k. 12 From this it was concluded that SFAs over the following underlying algebras are efficiently learnable: Boolean algebras over finite domains, equality algebra, tree automata algebra, and SFAs algebra. Efficient learning of SFAs over a monotonic algebra using mqs and eqs was established in [CDYS17], which improved the results of [MM14, MM17] by using a binary search instead of a helpful teacher.…”

Inferring Symbolic Automata

“…There already exists substantial literature on learning restricted forms of SFAs [GJL10, MM14, ASKK16, MM17, CDYS17], as well as general SFAs [DD17,AD18], and even nondeterministic residual SFAs [CHYS19]. For other types of automata over infinite alphabets, [HSM11] suggests learning abstractions, and [She19] presents a learning algorithm for deterministic variable automata.…”