Learning residual alternating automata

Abstract

Residuality plays an essential role for learning finite automata. While residual deterministic and nondeterministic automata have been understood quite well, fundamental questions concerning alternating automata (AFA) remain open. Recently, Angluin, Eisenstat, and Fisman (2015) have initiated a systematic study of residual AFAs and proposed an algorithm called AL⋆ – an extension of the popular L⋆ algorithm – to learn AFAs. Based on computer experiments they conjectured that AL⋆ produces residual AFAs, but have not been able to give a proof. In this paper we disprove this conjecture by constructing a counterexample. As our main positive result we design an efficient learning algorithm, named AL⋆⋆, and give a proof that it outputs residual AFAs only. In addition, we investigate the succinctness of these different finite automata (FA) types in more detail.