用平滑证明搜索桥接布尔和定量综合

Swarat Chaudhuri, Martin Clochard, Armando Solar-Lezama
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引用次数: 47

摘要

提出了一种布尔目标和定量目标下参数综合的新方法。该技术的输入是一个“草图”——一个缺少数值参数的程序——以及一个关于程序输入的概率假设。目标是自动合成参数的值,使生成的程序满足:(1){布尔规范},它声明程序必须满足某些断言,以及(2){定量规范},它为合成器期望优化的每个程序分配实值评级。我们的方法——称为平滑证明搜索——将这一任务简化为一系列无约束的平滑优化问题,然后用数值方法求解。通过迭代求解这些问题,我们得到了越来越接近布尔规范的参数值;在极限处,我们得到了可证明满足规范的值。这些近似是使用程序抽象的平滑的新概念来计算的,其中一个抽象的转换器是由一个根据抽象状态上的度量连续的函数来近似的。我们给出了我们的合成过程的原型实现,以及在嵌入式控制领域的两个基准上的实验结果。实验证明了平滑证明搜索优于不能同时满足布尔和定量合成目标的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bridging boolean and quantitative synthesis using smoothed proof search
We present a new technique for parameter synthesis under boolean and quantitative objectives. The input to the technique is a "sketch" --- a program with missing numerical parameters --- and a probabilistic assumption about the program's inputs. The goal is to automatically synthesize values for the parameters such that the resulting program satisfies: (1) a {boolean specification}, which states that the program must meet certain assertions, and (2) a {quantitative specification}, which assigns a real valued rating to every program and which the synthesizer is expected to optimize. Our method --- called smoothed proof search --- reduces this task to a sequence of unconstrained smooth optimization problems that are then solved numerically. By iteratively solving these problems, we obtain parameter values that get closer and closer to meeting the boolean specification; at the limit, we obtain values that provably meet the specification. The approximations are computed using a new notion of smoothing for program abstractions, where an abstract transformer is approximated by a function that is continuous according to a metric over abstract states. We present a prototype implementation of our synthesis procedure, and experimental results on two benchmarks from the embedded control domain. The experiments demonstrate the benefits of smoothed proof search over an approach that does not meet the boolean and quantitative synthesis goals simultaneously.
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