  We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic
nearest-neighbor Ising models with parallel dynamics. The probability P(t) that
a given spin has not flipped up to time t, when the system evolves from an
initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p
\simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0
models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies
the nature of dynamical scaling in the distribution of persistent sites
obtained under this dynamics.
