Learning Shuffle Ideals with Membership Queries and Contrastive Examples
This study investigates the learnability of shuffle ideals under membership and counter queries. To address the theoretical bottleneck that certain simple classes cannot be efficiently learned, this work integrates formal language theory with computational learning theory to propose novel structural conditions based on universal words and short lexicographic partitions, alongside corresponding algorithms. The primary contributions lie in delineating the boundaries of unlearnability for specific classes of shuffle ideals while demonstrating that efficient learning is achievable when the proposed structural conditions are satisfied. These findings offer a new perspective on combinatorial problems and deepen the understanding of learning complexity within query-based models.