--- res: bibo_abstract: - 'We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Peter foaf_name: Franek, Peter foaf_surname: Franek - foaf_Person: foaf_givenName: Marek foaf_name: Krcál, Marek foaf_surname: Krcál foaf_workInfoHomepage: http://www.librecat.org/personId=33E21118-F248-11E8-B48F-1D18A9856A87 bibo_doi: 10.1145/2751524 bibo_issue: '4' bibo_volume: 62 dct_date: 2015^xs_gYear dct_language: eng dct_publisher: ACM@ dct_title: Robust satisfiability of systems of equations@ ...