When boolean satisfiability meets gaussian elimination in a simplex way

Recent research on Boolean satisfiability (SAT) reveals modern solvers' inability to handle formulae in the abundance of parity (xor) constraints. Although xor-handling in SAT solving has attracted much attention, challenges remain to completely deduce xor-inferred implications and conflicts, to effectively reduce expensive overhead, and to directly generate compact interpolants. This paper integrates SAT solving tightly with Gaussian elimination in the style of Dantzig's simplex method. It yields a powerful tool overcoming these challenges. Experiments show promising performance improvements and efficient derivation of compact interpolants, which are otherwise unobtainable.