  Consider an irreducible, Harris recurrent Markov chain of transition kernel
{\Pi} and invariant probability measure {\pi}. If {\Pi} satisfies a
minorization condition, then the split chain allows the identification of
regeneration times which may be exploited to obtain perfect samples from {\pi}.
Unfortunately, many transition kernels associated with complex Markov chain
Monte Carlo algorithms are analytically intractable, so establishing a
minorization condition and simulating the split chain is challenging, if not
impossible. For uniformly ergodic Markov chains with intractable transition
kernels, we propose two efficient perfect simulation procedures of similar
expected running time which are instances of the multigamma coupler and an
imputation scheme. These algorithms overcome the intractability of the kernel
by introducing an artificial atom and using a Bernoulli factory. We detail an
application of these procedures when {\Pi} is the recently introduced iterated
conditional Sequential Monte Carlo kernel. We additionally provide results on
the general applicability of the methodology, and how Sequential Monte Carlo
methods may be used to facilitate perfect simulation and/or unbiased estimation
of expectations with respect to the stationary distribution of a non-uniformly
ergodic Markov chain.
