🤖 AI Summary
This study addresses the challenge of efficiently generating personalized corrective feedback from student-submitted finite automata under pedagogical constraints. To this end, this work proposes a novel tree-encoding technique that, for the first time, finitely represents the complete set of automaton corrections recognizing a given regular language as a regular tree language. Furthermore, a filtering mechanism is introduced to select correction candidates satisfying specific instructional requirements. By overcoming the computational bottlenecks inherent in traditional correction enumeration, the proposed approach enables the automated derivation and extraction of high-quality, personalized pedagogical feedback from erroneous student submissions. Consequently, this research establishes both a theoretical foundation and a practical toolset for advancing intelligent tutoring systems in formal language education.
📝 Abstract
Motivated by educational applications, we study the problem of computing all corrections that transform a finite automaton into one recognizing a given regular language L. We show that for deterministic finite automata the set of all corrections can be finitely characterized as a regular tree language. The construction is based on a tree encoding of all deterministic finite automata recognizing L, which is extended to correction trees that make individual corrections and their induced edit-operations explicit. Leveraging the closure properties of regular tree languages, we introduce so-called filters for selecting corrections satisfying didactic constraints, enabling the derivation of individualized feedback from student submissions.