Extraction of a computer-certified SMT solver for nonlinear theories

We present an effective procedure for solving of the so-called $\delta-$satisfiability modulo theory (SMT) problem over the reals. Our methods are supported by the special approach to the exact real arithmetic: constructive analysis. First, we present an alternative proof of the decidability of the bounded $\delta-$SMT problem within our framework and an efficient branch-and-bound algorithm, which is based on the rational interval arithmetic. We provide some initial experiments to demonstrate the applicability of the derived solver. Finally, we discuss potential extensions and possible optimizations of the suggested algorithm.