  We propose a new automaton model, called quantified data automata over words,
that can model quantified invariants over linear data structures, and build
poly-time active learning algorithms for them, where the learner is allowed to
query the teacher with membership and equivalence queries. In order to express
invariants in decidable logics, we invent a decidable subclass of QDAs, called
elastic QDAs, and prove that every QDA has a unique
minimally-over-approximating elastic QDA. We then give an application of these
theoretically sound and efficient active learning algorithms in a passive
learning framework and show that we can efficiently learn quantified linear
data structure invariants from samples obtained from dynamic runs for a large
class of programs.
