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We present the architecture of an elementary gene-finding algorithm that is based on a Variable Order Markov model (VOM). The VOM model is a generalization of the traditional Markov model that can cope with varying memory dependencies. The VOM model is more efficient in terms of its parameterization and therefore can be trained on relatively short sequences. Experiments with the proposed gene-finder (GF) on three prokaryotic genomes indicate its potential advantage on the detection of short genes.