Exploring the Relationship between the Structural and the Actual Similarities of Automata

Abstract

One of the most common representations of formal languages is deterministic finite-state automata. In recent years, a bunch of papers dedicated to the problem of synthesizing such an automaton by a list of positive and negative examples of some formal language was published. Many of proposed models try to construct candidate automaton, which is believed to somehow approximate the target one. In this paper, we exploring the relationship between the structural similarity of candidate and target finite-state automata and the percentage of common words in their formal languages. We formalize two different notions of automata similarity, and present the results of their comparison and draw conclusions regarding the applicability of these definitions to the problem of grammar inference.