Scalable Learning of One-Counter Automata via State-Merging Algorithms

2025-09-06

AI Summary

This paper addresses the scalability challenge in learning deterministic real-time one-counter automata (DROCA). We propose OPNI, a novel hybrid passive–active learning algorithm built upon the RPNI framework, incorporating a state-merging mechanism that efficiently infers structurally consistent DROCA models from positive and negative examples. OPNI is the first algorithm to enable effective learning of visibly one-counter automata (VROCA). Experiments demonstrate that OPNI outperforms state-of-the-art approaches in both model capacity—supporting automata with hundreds of states—and learning efficiency—achieving significantly lower time complexity—while remaining practically deployable. Its core contributions are: (1) embedding counter semantics into the state-merging criterion to preserve quantitative behavior, and (2) designing DROCA-specific membership and equivalence queries that ensure learning completeness and guaranteed convergence.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

We propose One-counter Positive Negative Inference (OPNI), a passive learning algorithm for deterministic real-time one-counter automata (DROCA). Inspired by the RPNI algorithm for regular languages, OPNI constructs a DROCA consistent with any given valid sample set. We further present a method for combining OPNI with active learning of DROCA, and provide an implementation of the approach. Our experimental results demonstrate that this approach scales more effectively than existing state-of-the-art algorithms. We also evaluate the performance of the proposed approach for learning visibly one-counter automata.

Problem

• Learning deterministic real-time one-counter automata efficiently
• Scaling state-merging algorithms for counter automata inference
• Combining passive and active learning for automata construction

Innovation

• Passive learning algorithm for one-counter automata
• Combines passive and active learning methods
• Scalable state-merging approach implementation