[Paper Review] Verifying Complex Systems Probabilistically through Learning, Abstraction and Refinement.

Jingyi Wang, Jun Sun+1 more|arXiv (Cornell University)|Oct 20, 2016

Formal Methods in Verification5 citations

TL;DR

This paper proposes LAR, a probabilistic verification method for complex systems that learns models from system traces instead of requiring precise upfront modeling. By combining learning, abstraction, and refinement, LAR generates either a bounded-confidence counterexample or a probabilistic model that serves as a proof obligation for property verification, with evaluations showing effectiveness on benchmarks and a real-world water purification system.

ABSTRACT

Precisely modeling complex systems like cyber-physical systems is often challenging, which may render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to `verify' such complex systems through a combination of learning, abstraction and refinement. Instead of starting with system modeling, our method takes a set of concrete system traces as input. The output is either a counterexample with a bounded probability of being a spurious counterexample, or a probabilistic model based on which the given property is `verified'. The model could be viewed as a proof obligation, i.e., the property is verified if the model is correct. It can also be used for subsequent system analysis activities like runtime monitoring. Our method has been implemented as a self-contained software toolkit. The evaluation on multiple benchmark systems as well as a real-world water purification system show promising results.

Motivation & Objective

• To address the challenge of verifying complex cyber-physical systems where precise modeling is impractical.
• To reduce reliance on manual, error-prone system modeling by learning system behavior directly from traces.
• To provide a probabilistic verification framework that bounds the risk of spurious counterexamples.
• To enable downstream analysis such as runtime monitoring by generating a reliable probabilistic model.
• To demonstrate practical applicability through evaluation on real-world and benchmark systems.

Proposed method

• The method takes a set of concrete system traces as input, bypassing the need for explicit system modeling.
• It uses learning techniques to infer a probabilistic model from the observed traces.
• Abstraction is applied to simplify the model while preserving relevant behavioral properties.
• Refinement iteratively improves the model and counterexample quality by focusing on discrepancies.
• The framework integrates learning, abstraction, and refinement in a feedback loop to enhance verification confidence.
• The output is either a counterexample with a bounded probability of being spurious or a probabilistic model that acts as a proof obligation for the property.

Experimental results

Research questions

• RQ1 Can a system be verified without requiring a precise, manually authored model?
• RQ2 How can learning from system traces be combined with abstraction and refinement to improve verification reliability?
• RQ3 What is the maximum probability of a spurious counterexample that can be tolerated in practice?
• RQ4 Can the inferred probabilistic model be used for subsequent system analysis tasks like runtime monitoring?
• RQ5 How effective is the method on real-world complex systems such as cyber-physical systems?

Key findings

• The LAR method successfully verifies system properties using only system traces, eliminating the need for detailed modeling.
• The approach produces counterexamples with a bounded probability of being spurious, providing confidence in results.
• The probabilistic model generated can serve as a proof obligation, enabling further analysis and validation.
• Evaluation on benchmark systems demonstrates the method’s feasibility and scalability.
• A real-world water purification system was successfully analyzed, confirming the method’s practical applicability.