Learning from equivalence queries and negative data

Four classical kinds of information sources that are consulted in formal language learning processes as studied in the area of Grammatical Inference are the following: Membership queries, equivalence queries, finite subsets of the target language (positive samples), and finite subsets of its complement (negative samples). One of the language classes that have been studied most thoroughly so far with respect to their algorithmical learnability is the class of regular languages. Motivated by the study of existing algorithms for the finite polynomial inference of a regular language from two of these sources we briefly address the remaining two-place combinations and then concentrate on one of them, namely the one joining equivalence queries with finite negative data. As the main purpose of this paper, we present a concrete learning algorithm which is able to identify a regular language in this setting and has polynomial complexity with respect to the size of the input set of negative data, the minimal DFA recognizing the target language, and the length of the given counterexamples.