2025/10/06 by Idan Attias, Attias, Idan, Lev Reyzin +5 · 1 voice · 1 citation
Computer Science · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Natural Language Processing Techniques #Text and Document Classification Technologies #cs.CC #cs.LG
paper · pdf · doi:10.48550/arxiv.2510.04834
openalex publication_date 2025/10/06 · arxiv published 2025/10/06 · arxiv updated 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28
Despite the theoretical significance and wide practical use of regular expressions, the computational complexity of learning them has been largely unexplored. We study the computational hardness of improperly learning regular expressions in the PAC model and with membership queries. We show that PAC learning is hard even under the uniform distribution on the hypercube, and also prove hardness of distribution-free learning with membership queries. Furthermore, if regular expressions are extended with complement or intersection, we establish hardness of learning with membership queries even under the uniform distribution. We emphasize that these results do not follow from existing hardness results for learning DFAs or NFAs, since the descriptive complexity of regular languages can differ exponentially between DFAs, NFAs, and regular expressions.