Probing the arrangement of hyperplanes (Q1842647)

The paper contains results about the combinatorial complexity of the geometry and topology related to an arrangement \(H\) of hyperplanes, obtained by the operation of ``probing'' by a flat \(F\) (using the respective intersection of \(H\) and \(F)\). In particular, the worst-case number of fixed direction line probes and those of flat probes to determine a generic line of \(H\) and \(H\) itself are obtained. Furthermore, interesting applications and connections to other areas are discussed, such as computational learning theory, networks of threshold functions, finger probing for polyhedral sets, robotics in general, and others.