On the inference of finite state automata from positive and negative data

Abstract

The works by Thrakhtenbrot–Barzdin and Gold can be considered to be the first works on the identification of Finite Automata from given data. The main drawback of their results is that they may obtain hypotheses that may be inconsistent with the provided data. This drawback was solved by the RPNI and Lang algorithms. Aside from these works, other works have introduced more efficient algorithms with respect to the training data. The direct consequence of this improvement has lead to algorithms that have lower error rates. Recently, some works have tackled the identification of NFAs instead of using the traditional DFA model. In this line of research, the inference of Residual Finite State Automata (RFSA) provides a canonical non–deterministic model. Other works consider the inference of teams of NFAs to be a method that is suitable to solve the grammatical inference of finite automata.We review the main approaches that solve the inference of finite automata by using positive and negative data from the target language. In this review, we will describe the above-mentioned formalisms and induction techniques.