# On Solving Quantified Bit-Vectors using Invertibility Conditions

arXiv: https://arxiv.org/abs/1804.05025 · HTML: https://mlsanity.com/paper/1804.05025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Solving Hard Mizar Problems with Instantiation and Strategy Invention](https://mlsanity.com/paper/2406.17762/) (2024)

## Abstract (arXiv)

We present a novel approach for solving quantified bit-vector formulas in Satisfiability Modulo Theories (SMT) based on computing symbolic inverses of bit-vector operators. We derive conditions that precisely characterize when bit-vector constraints are invertible for a representative set of bit-vector operators commonly supported by SMT solvers. We utilize syntax-guided synthesis techniques to aid in establishing these conditions and verify them independently by using several SMT solvers. We show that invertibility conditions can be embedded into quantifier instantiations using Hilbert choice expressions, and give experimental evidence that a counterexample-guided approach for quantifier instantiation utilizing these techniques leads to performance improvements with respect to state-of-the-art solvers for quantified bit-vector constraints.