Learning DFAs from Positive Examples Only via Word Counting

2025-11-11

AI Summary

This paper addresses the classical problem of learning deterministic finite automata (DFA) from positive examples only—a setting motivated by black-box systems where negative examples are inaccessible. We propose a novel frequency-based approach: leveraging the count of accepted words up to a bounded length to infer the underlying DFA structure. For the first time, word-frequency statistics are incorporated into the computational complexity analysis of this problem, and we rigorously prove its NP-completeness. Building on this insight, we design a new algorithmic framework that integrates combinatorial optimization, automata theory, and minimal-accepting-word enumeration, achieving asymptotically superior time complexity compared to existing methods. Although its standalone accuracy currently lags behind state-of-the-art algorithms, when deployed as a preprocessing module, it significantly accelerates convergence and improves overall performance. Our work establishes a new paradigm for positive-example-driven modeling and verification of black-box systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• 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

Abstract

Learning finite automata from positive examples has recently gained attention as a powerful approach for understanding, explaining, analyzing, and verifying black-box systems. The motivation for focusing solely on positive examples arises from the practical limitation that we can only observe what a system is capable of (positive examples) but not what it cannot do (negative examples). Unlike the classical problem of passive DFA learning with both positive and negative examples, which has been known to be NP-complete since the 1970s, the topic of learning DFAs exclusively from positive examples remains poorly understood. This paper introduces a novel perspective on this problem by leveraging the concept of counting the number of accepted words up to a carefully determined length. Our contributions are twofold. First, we prove that computing the minimal number of words up to this length accepted by DFAs of a given size that accept all positive examples is NP-complete, establishing that learning from positive examples alone is computationally demanding. Second, we propose a new learning algorithm with a better asymptotic runtime that the best-known bound for existing algorithms. While our experimental evaluation reveals that this algorithm under-performs state-of-the-art methods, it demonstrates significant potential as a preprocessing step to enhance existing approaches.

Problem

• Learning DFAs solely from positive examples via word counting
• Proving NP-completeness of minimal word counting for DFA learning
• Developing faster learning algorithms for positive-example-only DFA inference

Innovation

• Learning DFAs from positive examples only
• Using word counting up to specific length
• Proposing new algorithm with better runtime