Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems

Abstract

We propose a novel integration of interval constraint propagation (ICP) with SMT solvers for linear real arithmetic (LRA) to decide nonlinear real arithmetic problems. We use ICP to search for interval solutions of the nonlinear constraints, and use the LRA solver to either validate the solutions or provide constraints to incrementally refine the search space for ICP. This serves the goal of separating the linear and nonlinear solving stages, and we show that the proposed methods preserve the correctness guarantees of ICP. Experimental results show that such separation is useful for enhancing efficiency.