Partition-Refining Algorithms for Learning Finite State Automata

Abstract

Regular language learning from positive examples alone is infeasible. Subclasses of regular languages, though, can be inferred from positive examples only. The most common approach for learning such is the specific-to-general technique of merging together either states of an initial finite state automaton or nonterminals in a regular grammar until convergence.

In this paper we seek to unify some language learning approaches under the general-to-specific learning scheme. In automata terms it is implemented by refining the partition of the states of the automaton starting from one block until desired decomposition is obtained; i.e., until all blocks in the partition are uniform according to the predicate determining the properties required from the language.

We develop a series of learning algorithms for well-known classes of regular languages as instantiations of the same master algorithm. Through block decomposition we are able to describe in the same scheme, e.g., the learning by rote approach of minimizing the number of states in the automaton and inference of k-reversible languages.

Under the worst-case analysis partition-refinement is less efficient than alternative approaches. However, for many cases it turns out more efficient in practice. Moreover, it ensures the inference of the canonical automaton, whereas the state-merging approach will leave excessive states to the final automaton without a separate minimization step.