Software Testing in Computable Analysis

We initiate research on software testing in the realm of computable analysis over the real numbers and general topological spaces. The goal is to develop a general framework and to show some first results of testing algorithms for checking probabilistically whether a Type-2 machine approximately performs the task it is supposed to. We give a testing algorithm for Type-2 programs supposed to compute the exponential function. As main result, we design a test whether a program approximately computes a univariate polynomial of given degree. Its analysis reveals close relations to computational learning theory.