Learning Regular Languages via Alternating Automata

Nearly all algorithms for learning an unknown regular language, in particular the popular L∗ algorithm, yield deterministic finite automata. It was recently shown that the ideas of L∗ can be extended to yield non-deterministic automata, and that the respective learning algorithm, NL∗, outperforms L∗ on randomly generated regular expressions. We conjectured that this is due to the existential nature of regular expressions, and NL∗ might not outperform L∗ on languages with a universal nature. In this paper we introduce UL∗ — a learning algorithm for universal automata (the dual of nondeterministic automata); and AL∗ — a learning algorithm for alternating automata (which generalize both universal and non-deterministic automata). Our empirical results illustrate the advantages and trade-offs among L∗, NL∗, UL∗ and AL∗.