[Paper Review] Active Learning of Mealy Machines with Timers

Véronique Bruyère, Bharat Garhewal+3 more|arXiv (Cornell University)|Mar 4, 2024

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper presents the first active learning algorithm for Mealy machines with timers (MMTs), extending the $L^\sharp$ algorithm to a timed setting. By exploiting the timing sensitivity of timeouts and using symbolic queries implemented via polynomially many concrete queries, the method efficiently learns race-avoiding MMTs—overcoming the exponential query cost of prior timed automaton learning approaches.

ABSTRACT

We present the first algorithm for query learning Mealy machines with timers in a black-box context. Our algorithm is an extension of the L# algorithm of Vaandrager et al. to a timed setting. We rely on symbolic queries which empower us to reason on untimed executions while learning. Similarly to the algorithm for learning timed automata of Waga, these symbolic queries can be realized using finitely many concrete queries. Experiments with a prototype implementation show that our algorithm is able to efficiently learn realistic benchmarks.

Motivation & Objective

• Address the challenge of learning timed systems with quantitative timing semantics in a black-box setting.
• Overcome the exponential query complexity of existing timed automaton learning algorithms by shifting to a model with timers instead of clocks.
• Enable efficient learning of realistic, complex systems where timing behavior is critical but models are unavailable.
• Leverage the structural simplicity of Mealy machines with timers (MMTs) to avoid complex guard and reset inference.
• Develop a scalable, practical learning framework for systems where timing behavior is observable through timeouts.

Proposed method

• Extend the $L^\sharp$ algorithm to support Mealy machines with timers (MMTs), which model systems with timers that decrement and trigger observable timeout events.
• Use symbolic queries based on the elementary languages of Maler & Pnueli [24], which abstract over timing constraints and are implemented using concrete queries.
• Implement each symbolic query using only a polynomial number of concrete queries by exploiting the 'wiggling' property: small timing perturbations of an input cause predictable changes in timeout timing.
• Leverage the fact that in MMTs, only the causal transition leading to a timeout needs to be identified, not the full guard and reset structure as in timed automata.
• Construct a hypothesis MMT by grouping states based on behavioral equivalence and using a renaming function to track timer propagation across transitions.
• Ensure soundness and completeness of the learned model by verifying that timer updates and timeouts are consistently mapped across equivalent states.

Experimental results

Research questions

• RQ1 Can active learning be effectively extended to Mealy machines with timers (MMTs) in a black-box setting?
• RQ2 Can the query complexity of learning timed systems be reduced from exponential to polynomial by using a timer-based model instead of clock-based timed automata?
• RQ3 To what extent can the timing sensitivity of timeouts be exploited to infer causal transitions efficiently?
• RQ4 Is the proposed algorithm scalable and effective on realistic, non-trivial system benchmarks?
• RQ5 How does the performance of the algorithm compare to existing approaches for learning timed automata?

Key findings

• The proposed algorithm achieves polynomial query complexity for learning MMTs, in contrast to the exponential complexity of Waga's algorithm for timed automata.
• The algorithm efficiently learns race-avoiding MMTs by exploiting the 'wiggling' property: small input timing changes induce predictable timeout timing shifts.
• A prototype implementation in Rust successfully learns realistic benchmarks, demonstrating practical scalability.
• The method avoids the complex guard and reset inference required in timed automata by focusing only on identifying which transition caused a timeout.
• Theoretical analysis confirms that the learned MMT is sound and complete under the assumption of consistent timer renaming and initialization.
• The approach generalizes to generalized MMTs (gMMTs), allowing for more flexible timer updates while preserving correctness and efficiency.