Optimized models and symmetry breaking for the NFA inference problem

Abstract

Grammatical inference is concerned with the study of algorithms for learning automata and grammars from words. We propose some models for learning Nondeterministic Finite Automaton (NFA) of size k from samples of words of the language and words not belonging to the language we want to describe. To this end, we formulate the problem as a SAT model trying to reduce the size of generated SAT instances.We propose new models to generate even smaller SAT instances. We also suggest some techniques for breaking some symmetries, hence reducing the search space, and consequently, speeding-up solving. We also achieved some experimental comparisons and we analyze our various model improvements and over-constraint propositions. Compared to [1], our models are easier and faster to solve. Compare to the parallel solver of [2], we find some new bounds for some instances for which the minimal size of NFA is not known yet.

Taking Advantage of a Very Simple Property to Efficiently Infer NFAs

“…Efficient decomposition of each word into a prefix and a suffix is crucial. In [12] and [14], we proposed various decomposition strategies. Here, we consider three of them: [15] with the fitness f defined as…”

“…The set of best suffixes is composed of the best suffixes (w.r.t. to ) that cover S (see [12] for more details).…”

“…• the Best prefix model (P k ) is built in a similar way as the Best suffix model, starting with a selection of the best prefixes [12].…”

“…Note that ILS f k (init) is used with 3 different initial splits: random split (ILS f k (r)), split based on best prefix (ILS f k (P k )), and split based on best suffix (ILS f k (S k )). These experiments were carried out on state-of-the-art instances, described in [12]. These instances can be divided into three categories corresponding to the sizes of the alphabet (2, 5, and 10).…”

“…In this paper, we do not want to improve a specific solver or to design an ad-hoc solver. On the contrary, we try to improve the SAT models starting from the models of [12]. More specifically, we focus on the results that can be obtained using a simple property: for a given sample S, if there is a k_NFA, there is also a (k + 1)_NFA.…”