SMT-Based Active Learning of Weighted Automata

2026-05-08

AI Summary

This work addresses the inefficiency and poor robustness of traditional Hankel/L*-based methods for learning nondeterministic weighted finite automata (WFAs). It proposes the first active learning framework that integrates SMT solving to infer minimal WFAs over arbitrary semirings, encompassing both finite and infinite domains. The algorithm is guaranteed to terminate with a correct and minimal WFA, and the paper establishes sufficient conditions ensuring such termination. Empirical evaluations demonstrate that the approach significantly outperforms existing baselines and state-of-the-art algorithms in terms of both the size of the learned automata and the number of queries posed to the teacher, thereby exhibiting superior learning efficiency and broader applicability across semiring structures.

Abstract

We present an SMT-based active learning algorithm for nondeterministic weighted automata (WFAs) as a practical and robust alternative to Hankel/L*-style methods. Our algorithm is parametric in a given semiring and, if it terminates, guaranteed to produce minimal WFAs. We prove partial correctness and provide a sufficient termination condition, which in particular implies termination for all finite semirings. Our extensive experimental evaluation shows that our algorithm is capable of learning numerous minimal WFAs over both finite and infinite semirings, vastly outperforms a naive baseline, and is competitive with a state-of-the-art algorithm while producing significantly smaller automata and requiring less interaction with the teacher.

Problem

• weighted automata
• active learning
• SMT
• semiring
• minimality

Innovation

• SMT-based learning
• weighted automata
• active learning
• semiring
• automata minimization