We consider the problem of automatically and efficiently computing models of constraints, in the presence of complex background theories such as floating-point arithmetic. Constructing models, or proving that a constraint is unsatisfiable, has various applications, for instance for automatic generation of test inputs. It is well-known that a naïve encoding of constraints into simpler theories (for instance, bit-vectors or propositional logic) often leads to a drastic increase in size, or that it is unsatisfactory in terms of the resulting space and runtime demands. We define a framework for systematic application of approximations in order to improve performance. Our method is more general than previous techniques in the sense that approximations that are neither under- nor over-approximations can be used, and it shows promising performance on practically relevant benchmark problems.

中文翻译：

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求解器和决策过程的近似框架

我们考虑在复杂的背景理论（如浮点算术）存在的情况下自动有效地计算约束模型的问题。构建模型或证明约束不可满足具有多种应用，例如用于自动生成测试输入。众所周知，将约束简单地编码为更简单的理论（例如，位向量或命题逻辑）通常会导致大小的急剧增加，或者在产生的空间和运行时需求方面并不令人满意。我们为近似值的系统应用定义了一个框架，以提高性能。我们的方法比以前的技术更通用，因为可以使用既不低于也不过度近似的近似值，