Probabilistic Bisimulation for Parameterized Anonymity and Uniformity Verification

2025-05-15

IEEE Transactions on Software Engineering

AI Summary

This work addresses the long-standing challenge of parameterized verification of security properties—such as anonymity and uniformity—in infinite families of finite-state probabilistic systems. Methodologically, it introduces the first decidable logical framework by embedding probabilistic bisimulation checking into first-order logic over regular structures and integrating language inference techniques to enable fully automatic synthesis of verification proofs. This approach overcomes the decidability barrier faced by existing fully automated methods in infinite parameterized settings, supporting parameterized equivalence verification of critical security properties. Experimental evaluation demonstrates successful fully automated verification of classic cryptographic protocols—including Crowds and Onion Routing—as well as randomized algorithms, thereby significantly extending the frontier of formal verification for probabilistic systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state probabilistic systems. Our framework is built upon the first-order theory of regular structures, which provides a decidable logic for reasoning about these systems. We show that essential properties like anonymity and uniformity can be encoded and verified within this framework in a manner aligning with the principles of deductive software verification, where systems, properties, and proofs are expressed in a unified decidable logic. By integrating language inference techniques, we achieve full automation in synthesizing candidate bisimulation proofs for anonymity and uniformity. We demonstrate the efficacy of our approach by addressing several challenging examples, including cryptographic protocols and randomized algorithms that were previously beyond the reach of fully automated methods.

Problem

• Verifies probabilistic parameterized system equivalence via bisimulation
• Encodes anonymity and uniformity in decidable logical framework
• Automates bisimulation proof synthesis for cryptographic protocols

Innovation

• Novel logical framework for probabilistic parameterized systems
• Decidable logic based on regular structures theory
• Automated synthesis of bisimulation proofs via language inference