Inference of Over-Constrained NFA of Size $$k+1$$ to Efficiently and Systematically Derive NFA of Size k for Grammar Learning

Abstract

Grammatical inference involves learning a formal grammar as a finite state machine or set of rewrite rules. This paper focuses on inferring Nondeterministic Finite Automata (NFA) from a given sample of words: the NFA must accept some words, and reject others. Our approach is unique in that it addresses the question of whether or not a finite automaton of size k exists for a given sample by using an overconstrained model of size k + 1. Additionally, our method allows for the identification of the automaton of size k when it exists. While the concept may seem straightforward, the effectiveness of this approach is demonstrated through the results of our experiments.