Optimization modulo theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or Pseudo-Boolean terms. However, many SMT and OMT applications, in particular from SW and HW verification, require handling bit-precise representations of numbers, which in SMT are handled by means of the theory of bit-vectors (\({{\mathcal {B}}}{{\mathcal {V}}}\)) for the integers and that of floating-point numbers (\(\mathcal {FP}\)) for the reals respectively. Whereas an approach for OMT with (unsigned) \({{\mathcal {B}}}{{\mathcal {V}}}\) objectives has been proposed by Nadel & Ryvchin, unfortunately we are not aware of any existing approach for OMT with \(\mathcal {FP}\) objectives. In this paper we fill this gap, and we address for the first time \(\text {OMT}\) with \(\mathcal {FP}\) objectives. We present a novel OMT approach, based on the novel concept of attractor and dynamic attractor, which extends the work of Nadel and Ryvchin to work with signed-\({{\mathcal {B}}}{{\mathcal {V}}}\) objectives and, most importantly, with \(\mathcal {FP}\) objectives. We have implemented some novel \(\text {OMT}\) procedures on top of OptiMathSAT and tested them on modified problems from the SMT-LIB repository. The empirical results support the validity and feasibility of our novel approach.

优化模理论 (OMT) 是 SMT 的重要扩展，它允许找到优化给定目标函数的模型，通常由线性算术或伪布尔项组成。然而，许多 SMT 和 OMT 应用程序，特别是软件和硬件验证，需要处理数字的位精确表示，这在 SMT 中是通过位向量理论处理的（\({{\mathcal {B}} }{{\mathcal {V}}}\) ) 分别用于整数和浮点数 ( \(\mathcal {FP}\) ) 用于实数。而使用（无符号）\({{\mathcal {B}}}{{\mathcal {V}}}\)Nadel & Ryvchin 提出了目标，不幸的是，我们不知道任何现有的 OMT 方法与\(\mathcal {FP}\)目标。在这篇论文中，我们填补了这个空白，我们第一次解决了\(\text {OMT}\)与\(\mathcal {FP}\)目标。我们提出了一种新颖的 OMT 方法，它基于吸引子和动态吸引子的新概念，将 Nadel 和 Ryvchin 的工作扩展到了有符号的\({{\mathcal {B}}}{{\mathcal {V}} }\)目标，最重要的是，使用\(\mathcal {FP}\)目标。我们在OptiMathSAT之上实现了一些新颖的\(\text {OMT}\)程序并针对来自 SMT-LIB 存储库的修改问题对它们进行了测试。实证结果支持我们的新方法的有效性和可行性。