SMT for Polynomial Constraints on Real Numbers

This paper preliminarily reports an SMT for solving polynomial inequalities over real numbers. Our approach is a combination of interval arithmetic (over-approximation, aiming to decide unsatisfiability) and testing (under-approximation, aiming to decide satisfiability) to sandwich precise results. In addition to existing interval arithmetic, such as classical intervals and affine intervals, we newly design Chebyshev Approximation Intervals, focusing on multiplications of the same variables, like Taylor expansions. When testing cannot find a satisfiable instance, this framework is designed to start a refinement loop by splitting input ranges into smaller ones (although this refinement loop implementation is left to future work). Preliminary experiments on small benchmarks from SMT-LIB are also shown.