Satisfiability of systems of equations of real analytic functions is quasi-decidable

Abstract

In this paper we consider the problem of checking whether a system of equations of real analytic functions is satisfiable, that is, whether it has a solution. We prove that there is an algorithm (possibly non-terminating) for this problem such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is robust. A system of equations of robust, if its satisfiability does not change under small perturbations. As a basic tool for our algorithm we use the notion of degree from the field of (differential) topology. © 2011 Springer-Verlag GmbH.