Domain testing is a well-known software testing technique. Although research tasks have been initiated in domain testing, automatic test data generation based on character string predicates has not yet been reported. This paper presents a novel approach to automatically generate ON-OFF test points for character string predicate borders associated with program paths, and describes a corresponding test data generator. Slices with respect to predicates on paths are constructed to calculate the current values of variables in the predicates via program slicing techniques. Each character element of variables in a character string predicate is dynamically determined in turn by function minimization so that the ON-OFF test points for the predicate border can be automatically generated. The preliminary experimental results show that this approach is promising and effective.