决策程序的一致性分析

Swarat Chaudhuri, Azadeh Farzan, Zachary Kincaid
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引用次数: 5

摘要

由于计算的数值精度有限和传感器输入的误差等原因,许多计算领域的应用都是在不确定的情况下进行离散决策。因此,由这样的程序做出的单个决策可能是不确定的,并在执行的不同点导致相互矛盾的决策。这意味着,一个本来正确的程序可能会沿着它不遵循理想语义的路径执行,在此过程中违反了程序的基本不变量。如果一个程序在决策不确定的情况下没有出现这个问题,那么它就被称为是一致的。在本文中,我们提出了一个完善的、自动的程序分析来验证程序在这个意义上是一致的。我们的分析证明,在程序执行过程中做出的每个决策都与执行过程中早期做出的决策是一致的。证明是通过生成一个不变量来完成的,该不变量抽象了在程序位置l结束的执行过程中做出的所有决策的集合,然后使用不动点约束求解器验证,当这些决策与在l处做出的新决策相结合时,不会产生矛盾。我们在计算几何中实现算法的程序集合上评估了我们的分析。众所周知,一致性是几何中一个关键的、经常被违反的、被彻底研究过的正确性属性,但我们的研究是对几何算法一致性的自动验证的第一次尝试。我们的基准套件包括凸包计算、三角测量和点定位算法的实现。在几乎所有不一致的示例中(除了两个例外),我们的分析能够在几分钟内验证一致性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Consistency analysis of decision-making programs
Applications in many areas of computing make discrete decisions under uncertainty, for reasons such as limited numerical precision in calculations and errors in sensor-derived inputs. As a result, individual decisions made by such programs may be nondeterministic, and lead to contradictory decisions at different points of an execution. This means that an otherwise correct program may execute along paths, that it would not follow under its ideal semantics, violating essential program invariants on the way. A program is said to be consistent if it does not suffer from this problem despite uncertainty in decisions. In this paper, we present a sound, automatic program analysis for verifying that a program is consistent in this sense. Our analysis proves that each decision made along a program execution is consistent with the decisions made earlier in the execution. The proof is done by generating an invariant that abstracts the set of all decisions made along executions that end at a program location l, then verifying, using a fixpoint constraint-solver, that no contradiction can be derived when these decisions are combined with new decisions made at l. We evaluate our analysis on a collection of programs implementing algorithms in computational geometry. Consistency is known to be a critical, frequently-violated, and thoroughly studied correctness property in geometry, but ours is the first attempt at automated verification of consistency of geometric algorithms. Our benchmark suite consists of implementations of convex hull computation, triangulation, and point location algorithms. On almost all examples that are not consistent (with two exceptions), our analysis is able to verify consistency within a few minutes.
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