A Polynomial Time Incremental LearningAlgorithmRajesh ParekhCodrin

We present an eecient incremental algorithm for learning deterministic nite state automata (DFA) from labeled examples and membership queries. This algorithm is an extension of Angluin's ID procedure to an incremental framework. The learning algorithm is intermittently provided with labeled examples and has access to a knowledgeable teacher capable of answering membership queries. The learner constructs an initial hypothesis from the given set of labeled examples and the teacher's responses to membership queries. If an additional example observed by the learner is inconsistent with the current hypothesis then the hypothesis is modiied minimally to make it consistent with the new example. The update procedure ensures that the modiied hypothesis is consistent with all examples observed thus far. The algorithm is guaranteed to converge to a minimum state DFA corresponding to the target when the set of examples observed by the learner includes a live complete set. We prove the convergence of this algorithm and analyze its time and space complexities. R esum e Nous donnons un algorithme incr emental eecace pour l'apprentissage d'au-tomates d' etats nis a partir d'exemples etiquet es et de demandes d'apparte-nance. Cet algorithme est une extension a un cadre incr emental de la proc edure ID d'Angluin. L'algorithme d'apprentissage ree coit de mani ere intermittente des exemples de mots etiquet es et a acc es a un ((professeur)) capable de r epondre a des questions d'appartenance au langage-cible. L'algorithme construit une hy-poth ese initiale a partir du jeu d'exemples donn es et des r eponses du professeur. Si un example suppl ementaire trouv e par l'algorithme contredit l'hypoth ese courante, alors celle-ci est modii ee de mani ere minimale, aan d' eliminer la contradiction. La proc edure de modiication assure la compatibilit e de la nou-velle hypoth ese avec tous les exemples pr ec edents. L'algorithme converge vers un automate d' etats nis minimal en nombre d' etats reconnaissant le langage-cible quand le jeu d'exemples trait es comprend un ensemble ((live complete)). Nous prouvons la convergence de cet algorithme et analysons ses complexit es en espace et temps. Abstract. We present an eecient incremental algorithm for learning deterministic nite state automata (DFA) from labeled examples and membership queries. This algorithm is an extension of Angluin's ID procedure to an incremental framework. The learning algorithm is intermittently provided with labeled examples and has access to a knowledgeable teacher capable of answering membership queries. The learner constructs an …