Learning Event-recording Automata Passively

2025-08-05

AI Summary

This paper addresses the passive learning of Event-Rate Automata (ERAs)—a formalism for timed languages—from symbolic timed words labeled as positive or negative examples. We propose LEAP, the first passive learning algorithm for ERAs, built upon a state-merging framework wherein merge feasibility is encoded as an SMT satisfiability problem. We prove this decision problem to be NP-complete and leverage off-the-shelf SMT solvers for efficient, exact merging. LEAP guarantees consistency with the input sample and is language-complete: it can infer any ERA-definable timed language. Experiments demonstrate that LEAP accurately reconstructs target ERAs across multiple benchmark instances, validating its effectiveness and scalability. Our core contribution is the establishment of the first theoretical foundation for passive learning of ERAs, yielding a decidable, implementable, and language-complete learning algorithm.

Technology Category

• Machine Learning: Active Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

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: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

This paper presents a state-merging algorithm for learning timed languages definable by Event-Recording Automata (ERA) using positive and negative samples in the form of symbolic timed words. Our algorithm, LEAP (Learning Event-recording Automata Passively), constructs a possibly nondeterministic ERA from such samples based on merging techniques. We prove that determining whether two ERA states can be merged while preserving sample consistency is an NP-complete problem, and address this with a practical SMT-based solution. Our implementation demonstrates the algorithm's effectiveness through examples. We also show that every ERA-definable language can be inferred using our algorithm with a suitable sample.

Problem

• Learning timed languages from symbolic timed words
• State-merging algorithm for Event-Recording Automata (ERA)
• NP-complete state merging solved via SMT-based approach

Innovation

• State-merging algorithm for learning timed languages
• SMT-based solution for NP-complete merging problem
• Passive learning with positive and negative samples