cf61eb66474f59f7c0a67a77c337b58a3bd87bef
Title
Symmetry-Aware Invariant Synthesis for Automatic Verification of Consensus Protocols
Problem Statement
Automatically generating inductive invariants for consensus protocols like Paxos remains challenging, especially for unbounded instances. Current approaches often rely on predefined templates or manual guidance to search for invariants, limiting their effectiveness and generalizability.
Motivation
Structural symmetries in Paxos specifications, such as spatial and temporal regularities, can be leveraged to guide invariant synthesis more effectively. By exploiting these symmetries, we can potentially discover compact, generalizable invariants without relying on predefined templates, leading to more efficient and robust verification of consensus protocols.
Proposed Method
We propose a symmetry-aware invariant synthesis algorithm that exploits the structural features in Paxos-like protocols. The key steps are: 1) Identify the symmetry group of the protocol using automated static analysis. 2) Construct a symmetry-reduced abstract transition system. 3) Generate candidate invariants using counterexample-guided abstraction refinement (CEGAR). 4) Iteratively refine candidates by checking against concrete protocol executions and generalizing counterexamples across symmetry orbits. 5) Lift synthesized invariants back to the full state space by applying symmetry transformations.
Step-by-Step Experiment Plan
Step 1: Protocol Specification
Implement formal specifications for Paxos, Multi-Paxos, and Raft using a suitable formal language (e.g., TLA+). Ensure the specifications capture the essential behaviors and state spaces of these protocols.
Step 2: Symmetry Group Identification
Develop an automated static analysis tool to identify symmetry groups in the protocol specifications. This tool should detect spatial symmetries (e.g., permutations of process IDs) and temporal symmetries (e.g., message reordering).
Step 3: Symmetry-Reduced Abstraction
Implement an algorithm to construct a symmetry-reduced abstract transition system based on the identified symmetry groups. This should significantly reduce the state space while preserving essential protocol behaviors.
Step 4: CEGAR-based Invariant Generation
Develop a CEGAR-based algorithm for generating candidate invariants in the reduced abstract system. Use an SMT solver (e.g., Z3) for checking satisfiability and generating counterexamples.
Step 5: Counterexample Generalization
Implement a mechanism to generalize counterexamples across symmetry orbits. This should allow the algorithm to learn from a single counterexample and apply the knowledge to symmetric states.
Step 6: Invariant Refinement
Create an iterative refinement process that checks candidate invariants against concrete protocol executions and refines them based on the generalized counterexamples.
Step 7: Symmetry-based Lifting
Develop a procedure to lift the synthesized invariants from the reduced abstract system back to the full state space by applying symmetry transformations.
Step 8: Evaluation
Compare the performance of our symmetry-aware approach against state-of-the-art invariant synthesis tools like IC3PO and I4. Metrics should include invariant discovery time, compactness of invariants, and generalization to larger protocol instances.
Step 9: Analysis
Conduct an in-depth analysis of how different structural features in the specifications impact the effectiveness of our symmetry-guided approach. This may involve creating variants of the protocols with different symmetry properties.
Test Case Examples
Baseline Method Input
Paxos protocol specification in TLA+
Baseline Method Expected Output
A set of invariants for Paxos, potentially large and not generalizable to different instance sizes
Proposed Method Input
Paxos protocol specification in TLA+
Proposed Method Expected Output
A compact set of symmetry-aware invariants for Paxos, generalizable across different instance sizes
Explanation
The proposed method leverages symmetries to produce more compact and generalizable invariants, whereas baseline methods may struggle with scalability and generalization to different instance sizes.
Fallback Plan
If the proposed symmetry-aware method doesn't significantly outperform baselines, we can pivot to an analysis paper. We would focus on understanding why symmetry exploitation didn't yield the expected benefits. This could involve a detailed examination of the symmetries present in consensus protocols and how they interact with invariant properties. We could analyze the trade-offs between symmetry reduction and invariant expressiveness, potentially uncovering insights about the fundamental nature of consensus protocol verification. Additionally, we could explore hybrid approaches that combine symmetry-aware techniques with other invariant synthesis methods, aiming to leverage the strengths of multiple approaches.