  Pseudo-splines form a family of subdivision schemes that provide a natural
blend between interpolating schemes and approximating schemes, including the
Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function
approach, we derive expressions for the symbols of the symmetric $m$-ary
pseudo-spline subdivision schemes. We show that their masks have positive
Fourier transform, making it possible to compute the exact H\"older regularity
algebraically as a logarithm of the spectral radius of a matrix. We apply this
method to compute the regularity explicitly in some special cases, including
the symmetric binary, ternary, and quarternary pseudo-spline schemes.
