On using an inexact floating-point LP solver for deciding linear arithmetic in an SMT solver

Off-the-shelf linear programming (LP) solvers trade soundness for speed: for efficiency, the arithmetic is not exact rational arithmetic but floating-point arithmetic. As a side-effect the results come without any formal guarantee and cannot be directly used for deciding linear arithmetic. In this work we explain how to design a sound procedure for linear arithmetic built upon an inexact floating-point LP solver. Our approach relies on linear programming duality to instruct a black-box off-the-shelf LP solver to output, when the problem is not satisfiable, an untrusted proof certificate. We present a heuristic postprocessing of the certificate which accommodates for certain numeric inaccuracies. Upon success it returns a provably correct proof witness that can be independently checked. Our preliminary results are promising. For a benchmark suite extracted from SMT verification problems the floating-point LP solver returns a result for which proof witnesses are successfully and efficiently generated.