A Generic Algorithm for Learning Symbolic Automata from Membrship Queries

We present a generic algorithmic scheme for learning languages defined over large or infinite alphabets such as bounded subsets of N and R, or Boolean vectors of high dimension. These languages are accepted by deterministic symbolic automata that use predicates to label transitions, forming a finite partition of the alphabet for every state. Our learning algorithm, an adaptation of Angluin’s L∗, combines standard automaton learning by state characterization, with the learning of the static predicates that define the alphabet partitions. We do not assume a helpful teacher who provides minimal counter-examples when the conjectured automaton is incorrect. Instead we use random sampling to obtain PAC (probably approximately correct) learnability. We have implemented the algorithm for numerical and Boolean alphabets and the preliminary performance results show that languages over large or infinite alphabets can be learned under more realistic assumptions.