  Many SMT solvers implement efficient SAT-based procedures for solving
fixed-size bit-vector formulas. These approaches, 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 of non-fixed
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, this approach can still solve
many formulas by capitalizing on advancements 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 rewrites.
