  We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state
ferromagnetic Potts models evolving under parallel dynamics at zero temperature
from an initially disordered state, where \theta_p(q) is the persistence
exponent for parallel dynamics and \theta_s(q) = -{1/8}+
\frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the
persistence exponent under serial dynamics. This result is a consequence of an
exact, albeit non-trivial, mapping of the evolution of configurations of Potts
spins under parallel dynamics to the dynamics of two decoupled reaction
diffusion systems.
