New bounds for the query complexity of an algorithm that learns DFAs with correction and equivalence queries

Abstract

In this note, we show that the number of equivalence queries asked by an algorithm proposed in Becerra-Bonache et al. (Proceedings of the 8th International Colloquium on Grammatical Inference (ICGI ’06), Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin 2006) that learns deterministic finite automata with correction and equivalence queries is at most the injectivity degree of the target language, a notion that corresponds to the number of repetitions among the correcting words of all the elements in the quotient of that language by the Myhill-Nerode equivalence. Further, we propose a tight upper bound for the number of correction queries as a function which depends on the index of the target language, the length of the longest counterexample returned by the teacher and the injectivity degree of the target language. However, the bounds obtained here for the number of CQs are optimal for the LCA algorithm, and they do not represent a tight upper bound for DFA learning with EQs and CQs in general.