  In this paper a general approach for the perfect simulation of a stationary
process with at most countable state space is outlined. The process is
specified through a kernel, prescribing the probability of each state
conditional to the whole past history. We follow the seminal paper of Comets,
Fernandez and Ferrari, where sufficient conditions for the construction of a
certain perfect simulation algorithm have been given. We generalize this
approach by defining backward coalescence times for these kind of processes;
this allows us to construct perfect simulation algorithms under weaker
conditions.
