Synthesizing Proofs Using Proof Sharding and Exploration

2026-09-22

AI Summary

This study addresses the challenges of extensive manual intervention and limited scalability in the formal verification of distributed systems by proposing ProofSaX, a novel verification tool. ProofSaX pioneers a strategy that integrates proof sharding with controlled exploration, leveraging task decomposition and automated theorem proving to effectively mitigate state-space explosion and enable the automatic synthesis of correctness proofs. Experimental evaluation demonstrates that ProofSaX successfully synthesizes proofs for 86 out of 103 verification tasks, with individual runs requiring only one minute to two hours. These results indicate that the proposed approach significantly enhances verification efficiency while substantially reducing the costs associated with manual interaction.

Abstract

Distributed systems are hard to implement correctly, and subtle bugs can go undetected using traditional testing. Formal verification offers an alternative for proving the correctness of complex distributed systems. Despite previous efforts to automate and facilitate formal verification, it is still hard to integrate formal verification in software development. Programmers need to query the theorem prover repeatedly to find the correct proof of their system. This cycle of going back and forth with the theorem prover involves a lot of human intervention and is a barrier to adopting formal verification in software development. In this paper, we address the challenges of scaling formal verification in practice by reducing the human intervention required to find the correctness proof of a distributed system. We propose ProofSaX, an automated tool that shards large verification tasks and explores the proof search space for each shard independently to synthesize correctness proofs. We use controlled exploration when adding possible proof annotations to handle the search-space explosion problem. We evaluate ProofSaX on a variety of safety proofs for distributed systems. We show that ProofSaX can find the last proof annotation in 86 out of 103 proof-completion tasks, with runtimes ranging from one minute to two hours.

Problem

• formal verification
• distributed systems
• proof synthesis
• human intervention
• theorem prover

Innovation

• Formal Verification
• Proof Sharding
• Automated Proof Synthesis
• Controlled Exploration
• Distributed Systems