Reverse Mathematics Is Computable for Interval Computations

Abstract

For systems of equations and/or inequalities under interval uncertainty, interval computations usually provide us with a box whose all points satisfy this system. Reverse mathematics means finding necessary and sufficient conditions, i.e., in this case, describing the set of all the points that satisfy the given system. In this paper, we show that while we cannot always exactly describe this set, it is possible to have a general algorithm that, given $\varepsilon >0$, provides an $\varepsilon$-approximation to the desired solution set.