Can the perceptron classifier achieve perfect accuracy, on any data set?
The use of a nonlinear kernel never gives any guarantees to make any data set linearly separable in the higher dimensional feature space. Kernels are used to map the data from input space onto a higher dimensional space, in which a hyperplane will be better at separating the data (but no guarantee for linear separable higher dimensional mapped data). That is why we can not be sure that perceptron algorithm will work correctly on higher dimensional mapped dataset or not.