  The one-dimensional kinetic contact process with parallel update is
introduced and studied by the mean-field approximation and Monte Carlo (MC)
simulations. Contrary to a more conventional scenario with single active phase
for 1d models with Ising-like variables, we find two different adjacent active
phases in the parameter space of the proposed model with a second-order
transition between them and a multiphase point where the active and the
absorbing phases meet. While one of the active phases is quite standard with a
smooth average filling of the space-time lattice, the second active phase
demonstrates a very subtle (hidden) percolating order which becomes manifest
only after certain transformation from the original model. We determine the
percolation order parameter for active-active phase transition and discuss such
hidden orders in other low-dimensional systems. Our MC data demonstrate
finite-size critical and near-critical scaling of the order parameter
relaxation for the two phase transitions. We find three independent critical
indices for them and conclude that they both belong to the directed percolation
universality class.
