Formal Verification of Parameterized Systems based on Induction

2025-03-23

AI Summary

Verifying invariants with mixed universal/existential quantification in parameterized systems—such as cache-coherence and distributed protocols—remains challenging. This paper introduces WiseParaverifier, an counterexample-guided inductive verification framework. Its key contributions include: (i) the first counterexample-driven inductive procedure for such systems; (ii) a heuristic Generalize algorithm that efficiently synthesizes auxiliary invariants; (iii) support for quantifier lifting and merging to enhance expressiveness; and (iv) integration of symmetry reduction to accelerate invariant search. Combining SMT solving, quantified reasoning, and invariant synthesis, WiseParaverifier achieves fully automated verification on seven cache-coherence protocols and ten distributed protocols. It generates concise, human-readable proofs, demonstrates strong transferability across protocol families, and is pedagogically accessible for teaching formal verification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Privacy-enhancing technologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Parameterized systems play a crucial role in the computer field, and their security is of great significance. Formal verification of parameterized protocols is especially challenging due to its"parameterized"feature, which brings complexity and undecidability. Existing automated parameterized verification methods have limitations, such as facing difficulties in automatically deriving parameterized invariants constrained by mixed Forall and Exists quantifiers, or having challenges in completing the parameterized verification of large and complex protocols. This paper proposes a formal verification framework for parameterized systems based on induction, named wiseParaverifier. It starts from small concretizations of protocols, analyzes inductive counterexamples, and constructs counterexample formulas to guide the entire process of parameterized verification. It also presents a heuristic Generalize method to quickly find auxiliary invariants, a method for promoting complex mixed quantifiers and merging parameterized invariants, and uses symmetric reduction ideas to accelerate the verification process. Experimental results show that wiseParaverifier can successfully complete automatic inductive verification on 7 cache coherence protocols and 10 distributed protocols. It has strong verification capabilities and migration capabilities, and can provide concise and readable verification results, which is helpful for learners to understand protocol behaviors.

Problem

• Verifying security of parameterized systems with complexity
• Automating derivation of mixed quantifier invariants in protocols
• Scaling verification for large, complex distributed protocols

Innovation

• Induction-based framework for parameterized system verification
• Heuristic Generalize method for finding auxiliary invariants
• Symmetric reduction to accelerate verification process