Speeding up Quantified Bit-Vector SMT Solvers by Bit-Width Reductions and Extensions

Recent experiments have shown that satisfiability of a quantified bit-vector formula coming from practical applications almost never changes after reducing all bit-widths in the formula to a small number of bits. This paper proposes a novel technique based on this observation. Roughly speaking, a given quantified bit-vector formula is reduced and sent to a solver, an obtained model is then extended to the original bit-widths and verified against the original formula. We also present an experimental evaluation demonstrating that this technique can significantly improve the performance of state-of-the-art smt solvers Boolector, CVC4, and Q3B on quantified bit-vector formulas from the smt-lib repository.