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We describe a new algorithm for the perfect simulation of variable lengthMarkov chains and random systems with perfect connections. This algorithm,which generalizes Propp and Wilson's simulation scheme, is based on the idea ofcoupling into and from the past. It improves on existing algorithms by relaxingthe conditions on the kernel and by accelerating convergence, even in thesimple case of finite order Markov chains. Although chains of variable orinfinite order have been widely investigated for decades, their use in appliedprobability, from information theory to bio-informatics and linguistics, hasrecently led to considerable renewed interest.

Perfect Simulation Of Processes With Long Memory: A `Coupling Into And From The Past' Algorithm