Learning Residual Alternating Automata

Abstract

Residuality plays an essential role for learning finite automata. While residual deterministic and non-deterministic 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 have 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 FA types in more detail.

Guarded Kleene Algebra with Tests: Automata Learning

“…In the future, we would like to cover other examples, such as the canonical probabilistic RFSA [53] and the canonical alternating RFSA [28,17]. Probabilistic automata of the type in [53] are typically modelled as T F -coalgebras instead of F Tcoalgebras [81], and thus will need a shift in perspective.…”

“…Inside Academia The lack of a canonical target acceptor when learning nondeterministic models has lead to a number of independent approaches, for different variants of non-determinism [28,53]. More recently, there have been efforts to give a unifying perspective on those approaches.…”

“…A major challenge in learning non-deterministic models is the lack of a canonical target acceptor for a given language [49]. The problem has been independently approached for different variants of non-determinism, often with the idea of finding a subclass admitting a unique representative [53,28] such as the canonical RFSA, the minimal xor automaton, or the átomaton.…”

“…One of the main challenges in learning non-deterministic models such as NetKAT automata is the common lack of a unique minimal acceptor for a given language [49]. The problem has been independently approached for different variants of nondeterminism, often with the common idea of finding a subclass admitting a unique representative [53,28]. More general and unifying perspectives were given by van Heerdt [66,63,64] and Myers et al [119].…”