Query Learning of Minimal Deterministic Symbolic Finite Automata Separating Regular Languages

We propose a query learning algorithm for constructing a minimal DSFA M that separates given two regular languages \(L_+\) and \(L_-\) , i.e., \(L_+ \subseteq \mathcal {L}(M)\) and \(L_- \cap \mathcal {L}(M) = \emptyset \) . Our algorithm extends the algorithm for learning separating DFAs by Chen et al. (TACAS 2009) embedding the algorithm for learning DSFAs by Argyros and D’Antoni (CAV 2018). Since the problem of finding a minimal separating automaton is NP-hard, we also propose two heuristic methods to learn a separating DSFA which is not necessarily minimal. One runs faster and the other outputs smaller separating DSFAs. So, one of those can be chosen depending on the application requirement.