How can a classifier using lapacian kernel achieve no error on the input samples?


If we have a sample dataset $ S = \{(x_1, y_i),…(x_n,y_n)\}$ where $ y_i = \{0,1\}$ , how can we tune $ \sigma$ such that there is no error on $ S$ from a classifier using the Laplacian kernel?

Laplacian Kernel is

$ $ K(x,x’) = exp(-\dfrac{\| x – x’\|}{\sigma}) $ $

If this is true, does it mean that if we run hard-SVM with the Laplacian kernel and $ \sigma$ from the above on $ S$ , we can find no error separing classifier also?