Infinite State Model Checking by Learning Transitive Relations

2025-02-07

AI Summary

This work addresses the safety verification problem for infinite-state systems. We propose a diameter-finitization method based on learning disjunctive transitive relations and systematic state-space expansion: by combining recursive analysis with relation projection, our approach infers disjunctive (rather than solely conjunctive) transitive relations—overcoming a key limitation of prior techniques—and automatically extends the original system’s state space to ensure finite diameter, thereby reducing global safety to bounded reachability checking. Implemented in the tool LoAT, our method demonstrates, across diverse infinite-state systems—including counter programs and parameterized loops—verification efficiency and precision that match or exceed state-of-the-art approaches. Experimental results confirm substantial improvements in both automation and practicality for safety verification of infinite-state systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose a new approach for proving safety of infinite state systems. It extends the analyzed system by transitive relations until its diameter D becomes finite, i.e., until constantly many steps suffice to cover all reachable states, irrespective of the initial state. Then we can prove safety by checking that no error state is reachable in D steps. To deduce transitive relations, we use recurrence analysis. While recurrence analyses can usually find conjunctive relations only, our approach also discovers disjunctive relations by combining recurrence analysis with projections. An empirical evaluation of the implementation of our approach in our tool LoAT shows that it is highly competitive with the state of the art.

Problem

• Proving safety of infinite state systems
• Extending system by transitive relations
• Using recurrence analysis for transitive relations

Innovation

• Extends system by transitive relations
• Uses recurrence analysis for relations
• Combines recurrence with projection techniques