Decision procedures for SMT problems based on the theory of bit-vectors are a fundamental component in state-of-the-art software and hardware verifiers. While very efficient in general, certain SMT instances are still challenging for state-of-the-art solvers (especially when such instances include computationally costly functions). In this work, we present an approach for the quantifier-free bit-vector theory (QF_BV in SMT-LIB) based on incremental SMT solving and abstraction refinement. We define four concrete approximation steps for the multiplication, division and remainder operators and combine them into an incremental abstraction scheme. We implement this scheme in a prototype extending the SMT solver Boolector and measure both the overall performance and the performance of the single approximation steps. The evaluation shows that our abstraction scheme contributes to solving more unsatisfiable benchmark instances, including seven instances with unknown status in SMT-LIB.

中文翻译：

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用于解决位向量上的硬 SMT 实例的增量抽象方案

基于位向量理论的 SMT 问题决策程序是最先进的软件和硬件验证器的基本组成部分。虽然总体上非常有效，但某些 SMT 实例对于最先进的求解器仍然具有挑战性（尤其是当此类实例包含计算成本高的函数时）。在这项工作中，我们提出了一种基于增量 SMT 求解和抽象细化的无量词位向量理论（SMT-LIB 中的 QF_BV）的方法。我们为乘法、除法和余数运算符定义了四个具体的近似步骤，并将它们组合成一个增量抽象方案。我们在扩展 SMT 求解器 Boolector 的原型中实施该方案，并测量整体性能和单个近似步骤的性能。