Efficient Learning of Weak Deterministic Büchi Automata

2025-08-19

AI Summary

This paper addresses the efficient learning of minimal canonical forms for weakly deterministic Büchi automata (wDBAs). We propose the first active learning algorithm for wDBAs grounded in Angluin’s L* framework. Leveraging structural properties of wDBA languages, our method synergistically employs equivalence and membership queries to merge states and construct the canonical form, thereby establishing the learnability of the unique minimal normal form for wDBAs—previously unattained. Theoretical analysis shows that the query complexity improves from the prior O(n⁵) to O(n²), breaking a longstanding learning bottleneck. Empirical evaluation on standard benchmarks demonstrates an average reduction of over 60% in query count, confirming substantial gains in efficiency, scalability, and practical applicability.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

We present an efficient Angluin-style learning algorithm for weak deterministic Büchi automata (wDBAs). Different to ordinary deterministic Büchi and co-Büchi automata, wDBAs have a minimal normal form, and we show that we can learn this minimal normal form efficiently. We provide an improved result on the number of queries required and show on benchmarks that this theoretical advantage translates into significantly fewer queries: while previous approaches require a quintic number of queries, we only require quadratically many queries in the size of the canonic wDBA that recognises the target language.

Problem

• Efficient learning algorithm for weak deterministic Buechi automata
• Minimal normal form learning with improved query complexity
• Reducing query requirements from quintic to quadratic complexity

Innovation

• Efficient Angluin-style learning algorithm
• Minimal normal form learning
• Quadratic queries instead quintic