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Taking advantage of a very simple property to efficiently infer NFAs

Tomasz JastrzabFr\'ed\'eric Lardeux (LERIA)Eric Monfroy (LERIA)
Mar 2023
Grammatical inference consists in learning a formal grammar as a finite statemachine or as a set of rewrite rules. In this paper, we are concerned withinferring Nondeterministic Finite Automata (NFA) that must accept some words,and reject some other words from a given sample. This problem can naturally bemodeled in SAT. The standard model being enormous, some models based onprefixes, suffixes, and hybrids were designed to generate smaller SATinstances. There is a very simple and obvious property that says: if there isan NFA of size k for a given sample, there is also an NFA of size k+1. We firststrengthen this property by adding some characteristics to the NFA of size k+1.Hence, we can use this property to tighten the bounds of the size of theminimal NFA for a given sample. We then propose simplified and refined modelsfor NFA of size k+1 that are smaller than the initial models for NFA of size k.We also propose a reduction algorithm to build an NFA of size k from a specificNFA of size k+1. Finally, we validate our proposition with some experimentationthat shows the efficiency of our approach.