Many SMT solvers implement efficient SAT-based procedures for solving fixed-size bit-vector formulas. These techniques, however, cannot be used directly to reason about bit-vectors of symbolic bit-width. To address this shortcoming, we propose a translation from bit-vector formulas with parametric bit-width to formulas in a logic supported by SMT solvers that includes non-linear integer arithmetic, uninterpreted functions, and universal quantification. While this logic is undecidable, our approach can still solve many formulas that arise in practice by capitalizing on advances in SMT solving for non-linear arithmetic and universally quantified formulas. We provide several case studies in which we have applied this approach with promising results, including the bit-width independent verification of invertibility conditions, compiler optimizations, and bit-vector rewrite rules.

许多 SMT 求解器采用高效的基于 SAT 的程序来求解固定大小的位向量公式。然而，这些技术不能直接用于推理符号位宽的位向量。为了解决这个缺点，我们建议将具有参数位宽的位向量公式转换为 SMT 求解器支持的逻辑中的公式，其中包括非线性整数算术、未解释函数和通用量化。虽然这个逻辑是不可判定的，但我们的方法仍然可以通过利用 SMT 求解非线性算术和通用量化公式的进步来解决实践中出现的许多公式。我们提供了几个案例研究，其中我们应用了这种方法并取得了可喜的结果，包括可逆条件的位宽独立验证、编译器优化、