A Deeper Look at Depth: Stable Generation Accounting for Quantifier Reasoning

2026-09-22

AI Summary

本文针对SMT求解器在程序验证中因量词实例化深度计算方法导致的不稳定性问题，提出了一种新的稳定生成方法，并在Z3上实现，显著减少了结果波动。

Abstract

SMT solvers make automated verification convenient. At the same time, solvers suffer from instability, whereby seemingly inconsequential changes to the input may cause a previously quickly produced proof to fail or time out. This paper addresses a common cause of outcome instability (i.e., unsat/unknown fluctuations) in the context of program verification. We demonstrate that the generation (i.e., depth) accounting used to make quantifier instantiation practical and implemented in multiple state-of-the-art SMT solvers is non-confluent (i.e., prone to divergence), and that this leads to instability. We then address this deficiency and develop a new accounting method that is stable. The new method is justified using a sequence of refinements from an abstract, confluent solver model all the way to our implementation in Z3. Our empirical evaluation demonstrates that our implementation reduces outcome instability by 94% in the unstable core of the Mariposa benchmark without leading to performance regressions.

Problem

• SMT solvers
• outcome instability
• quantifier instantiation
• non-confluent
• program verification

Innovation

• Stable Generation
• Quantifier Reasoning
• SMT Solvers
• Confluence
• Outcome Instability