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Teoria Automatów


Active learning automata with syntactic queries

Prelegent: Jan Otop

2022-01-26 14:15

Regular languages can be actively learned with membership and equivalence queries in polynomial time. The learning algorithm, called the L^* algorithm, constructs iteratively the right congruence relation of a given regular language L, and returns the minimal DFA recognizing L. The L^* algorithm has been adapted to various types of automata: tree automata, weighted automata, nominal automata. However, an extension to infinite-word automata has been elusive. In this talk, I will present an extension of the active learning framework, in which the algorithm can ask syntactic queries about the automaton representing a given infinite-word language. First, I will discuss why extending L^*, which asks only semantic queries, to infinite-words languages is difficult. Next, I will present an alternative approach; instead of learning some automaton for a hidden language, we assume that there is a hidden automaton and the algorithm is supposed to learn an equivalent automaton. In this approach, the learning algorithm is allowed to ask standard semantic queries (membership and equivalence) and loop-index queries regarding the structure of the hidden automaton. These queries do not reveal the full structure of the automaton and hence do not trivialize the learning task. In the extended framework, there are polynomial-time learning algorithms for various types of infinite-word automata: deterministic Buechi automata, LimSup-automata, deterministic parity automata and limit-average automata. Finally, the idea to incorporate syntactic queries can be adapted to the pushdown framework; I will briefly discuss the learning algorithm for deterministic visibly pushdown automata.