Learning behaviors of automata from multiplicity and equivalence queries

Abstract

We consider the problem of identifying the behavior of an unknown automaton with multiplicity in the field Q of rational numbers (Q-automaton) from multiplicity and equivalence queries. We provide an algorithm which is polynomial in the size of the Q-automaton and of the maximum length of the given counterexamples. As a consequence, we have that Q-automata are PAC-learnable in polynomial time when multiplicity queries are allowed. A corollary of this result is that regular languages are polynomially predictable using membership queries w.r.t. the representation of unambiguous non-deterministic automata. This is important, as there are unambiguous automata such that the equivalent deterministic automaton has an exponentially larger number of states.KeywordsFormal Power SeriesFormal SeriesRegular LanguageFinite AutomatonFinite State AutomatonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.