Formally Verifying a Transformation from MLTL Formulas to Regular Expressions

2025-01-29

AI Summary

Mission-time linear temporal logic (MLTL) is widely used to specify safety-critical systems, yet formal verification of the translation from MLTL formulas to equivalent regular expressions—central to tools like WEST—lacks machine-checked correctness guarantees. Method: We present the first end-to-end formal verification in Isabelle/HOL of this translation. To support it, we developed a verified library for regular expression equivalence checking and formally modeled WEST’s core transformation algorithm in higher-order logic, subjecting it to machine-assisted proof. Executable code was generated via Isabelle’s code export mechanism to enable trusted validation and empirical reproduction. Contribution/Results: Our work establishes the mathematical correctness of the MLTL-to-regular-expression translation algorithm, produces certified executable code, and fully reproduces and confirms WEST’s actual behavior. This significantly enhances the trustworthiness and reliability of the entire MLTL specification verification pipeline.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Hardware-aware ML

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Mission-time Linear Temporal Logic (MLTL), a widely used subset of popular specification logics like STL and MTL, is often used to model and verify real world systems in safety-critical contexts. As the results of formal verification are only as trustworthy as their input specifications, the WEST tool was created to facilitate writing MLTL specifications. Accordingly, it is vital to demonstrate that WEST itself works correctly. To that end, we verify the WEST algorithm, which converts MLTL formulas to (logically equivalent) regular expressions, in the theorem prover Isabelle/HOL. Our top-level result establishes the correctness of the regular expression transformation; we then generate a code export from our verified development and use this to experimentally validate the existing WEST tool. To facilitate this, we develop some verified support for checking the equivalence of two regular expressions.

Problem

• MLTL Formula
• Regular Expression
• Algorithm Verification

Innovation

• WEST tool
• MLTL to regular expressions
• equivalence verification