A Myhill-Nerode Characterization and Active Learning for One-Clock Timed Automata

2026-01-21

AI Summary

This work addresses the long-standing absence of a Myhill–Nerode-style characterization for languages recognized by single-clock deterministic timed automata (1-DTA), a gap that has impeded the construction of canonical forms and the development of active learning algorithms. By introducing the notion of *semi-integer timed words* and their reset behaviors, the paper establishes a Myhill–Nerode-type equivalence relation tailored to 1-DTA, effectively resolving the non-canonicity issues arising from divergent clock-reset strategies along different paths. Building on this characterization, the authors devise an L*-style active learning algorithm capable of correctly inferring a canonical representation of a 1-DTA. This contribution provides the first theoretically grounded framework for the formal learnability of 1-DTA and yields the first active learning method with correctness guarantees for this class of timed systems.

Technology Category

• Machine Learning: Active Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

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

Abstract

We present a Myhill-Nerode style characterization for languages recognized by one-clock deterministic timed automata (1-DTA). Although there is only one clock, distinct automata may reset it differently along the same word. This adds a significant challenge in the search for a canonical automaton. Our characterization is based on a new perspective of 1-DTAs in terms of"half-integral"words that they accept, along with the reset information encoded by them. We apply our results to develop L* style algorithms that learn the canonical 1-DTA.

Problem

• Myhill-Nerode
• one-clock timed automata
• canonical automaton
• active learning
• timed languages

Innovation

• Myhill-Nerode characterization
• one-clock timed automata
• half-integral words
• active learning
• L* algorithm