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 non-deterministic 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^∗.