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Several methods have been developed to construct λ−free automata that represent a regular expression. Among the most widely known are the position automaton (Glushkov), the partial derivatives automaton (Antimirov) and the follow automaton (Ilie and Yu). All these automata can be obtained with quadratic time complexity, thus, the comparison criterion is usually the size of the resulting automaton. The methods that obtain the smallest automata (although, for general expressions, they are not comparable), are the follow and the partial derivatives methods. In this paper we propose another method to obtain a λ-free automaton from a regular expression. The number of states of the automata we obtain is bounded above by the size of both the partial derivatives automaton and of the follow automaton. Our algorithm also runs with the same time complexity of these methods.

A new version of the RPNI algorithm, called RPNI2, is presented. The main difference between them is the capability of the new one to extend the training set during the inference process. The effect of this new feature is specially notorious in the inference of languages generated from regular expressions and Non-deterministic Finite Automata (NFA). A first experimental comparison is done between RPNI2 and DeLeTe2, other algorithm that behaves well with the same sort of training data. 1

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