Automated Inference of Scalable and Interpretable Inductive Invariants for Distributed Protocols

핵심 개념

Inductive proof slicing is a new automated, compositional technique for inferring scalable and interpretable inductive invariants for verifying the safety of large-scale distributed protocols.

초록

The paper presents a new technique called inductive proof slicing for automated inference of inductive invariants for verifying the safety of distributed protocols. The key ideas are:

Inductive Proof Graph: The technique uses a core data structure called the inductive proof graph, which explicitly represents the lemma and action dependencies of an inductive invariant. This graph is built incrementally during the inference procedure, working backwards from the target safety property.

Localized Synthesis: The inference algorithm integrates localized syntax-guided lemma synthesis routines at nodes of the proof graph, which are accelerated by computation of localized grammar and state variable slices. This allows the technique to scale effectively to large distributed protocol verification tasks.

Interpretability: The decomposition provided by the proof graph structure allows failures of synthesis tasks during inference to be localized to small sub-components of the graph. This facilitates concrete and effective diagnosis and repair by a user, enhancing the interpretability of both the final inductive proof and the intermediate results.

The technique is evaluated on several complex distributed and concurrent protocols, including large-scale specifications of the Raft consensus protocol, demonstrating its effectiveness in scaling to problems beyond the capabilities of modern distributed protocol verification tools.

통계

The full set of reachable states explored by the algorithm for the SimpleConsensus protocol contains 110,464 distinct states when instantiated with finite parameters where |Node| = 3 and |Value| = 2.
When projected onto the variable slice {leader, decided}, this set of reachable states contains 10 distinct states, a 11,046x reduction.
The variable slice at the BecomeLeader action node of UniqueLeaders is {leader, votes}, which gives a projected state set of 94, a 1,175x reduction from the full reachable state set.

인용구

"Many techniques for automated inference of inductive invariants for distributed protocols have been developed over the past several years, but their performance can still be unpredictable and their failure modes opaque for large-scale verification tasks."
"In particular, one key drawback of these methods is that, in their current form, they are very much "all or nothing". That is, a given problem can either be automatically solved with no manual proof effort, or the problem falls outside the method's scope and a failure is reported. In the latter case, little assistance is provided in terms of how to develop a manual proof or how a human can offer guidance to the tool."

핵심 통찰 요약

Scalable, Interpretable Distributed Protocol Verification by Inductive Proof Slicing

by William Schu... 게시일 arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18048.pdf

더 깊은 질문

How can the inductive proof graph structure be extended to support interactive refinement and proof completion by a human user?

The inductive proof graph structure can be extended to support interactive refinement and proof completion by incorporating features that facilitate human intervention and guidance. One way to achieve this is by enhancing the interpretability of the graph, making it easier for a user to understand the dependencies between lemmas and actions. This can involve visual representations of the graph, highlighting critical paths or nodes that require attention.
Additionally, the graph can be augmented with annotations or comments that provide insights into the reasoning behind each lemma and its relation to the overall proof. These annotations can serve as cues for a user to identify areas of potential improvement or refinement. Furthermore, the graph can include interactive elements that allow a user to manipulate the structure, add new nodes or edges, and experiment with different proof strategies.
Moreover, the inductive proof graph can be integrated with a user-friendly interface that enables direct interaction with the graph. This interface could include functionalities such as drag-and-drop editing, real-time feedback on changes, and suggestions for next steps in the proof process. By enabling users to actively participate in the refinement and completion of the proof, the inductive proof graph becomes a collaborative tool for both automated and manual verification efforts.

What are the theoretical limits of the inductive proof slicing technique, and how do they compare to other automated invariant inference approaches?

Theoretical limits of the inductive proof slicing technique primarily revolve around the complexity of the protocols being verified and the scalability of the inference algorithm. One potential limit is the computational overhead associated with maintaining and updating the inductive proof graph as the size and intricacy of the protocol increase. This could lead to performance bottlenecks and challenges in handling large-scale systems with numerous states and actions.
Comparatively, other automated invariant inference approaches may have different theoretical limits. For instance, model checking algorithms like IC3/PDR may face challenges in handling highly nondeterministic systems or protocols with complex transition relations. Syntax-guided or enumerative invariant synthesis methods may struggle with scalability when dealing with protocols that have a large state space or intricate dependencies between variables.
In terms of scalability, the inductive proof slicing technique aims to address the limitations of existing approaches by leveraging the compositional structure of inductive invariants and utilizing localized synthesis routines. This can potentially improve the scalability of the technique compared to traditional methods by breaking down the inference process into smaller, more manageable tasks.

Could the inductive proof graph structure be applied to other domains beyond distributed protocol verification, such as program analysis or hardware design?

Yes, the inductive proof graph structure can be adapted and applied to various domains beyond distributed protocol verification, including program analysis and hardware design. In program analysis, the graph can represent the dependencies between program properties, loop invariants, and control flow actions. By decomposing the proof obligations into a graph structure, program analysts can visualize the logical relationships between different parts of the program and identify areas that require further investigation or refinement.
Similarly, in hardware design, the inductive proof graph can capture the dependencies between hardware components, state variables, and transition actions. This can aid in verifying the correctness of hardware designs, identifying potential bugs or inconsistencies, and guiding the refinement of the design specifications. The graph can serve as a roadmap for ensuring the integrity and reliability of complex hardware systems.
Overall, the flexibility and adaptability of the inductive proof graph structure make it a versatile tool that can be applied to a wide range of domains where formal verification and proof reasoning are essential. Its compositional nature and interpretability features make it a valuable asset in various verification and validation tasks beyond distributed protocols.