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Generalized stack decoding algorithms for statistical machine translation. Proceedings on the Workshop on Statistical Machine Translation, HLT-NAACL 2006, 2006. pp. 64-71.In this paper we propose a generalization of the Stack-based decoding paradigm for Statistical Machine Translation. The well known single and multi-stack decoding algorithms defined in the literature have been integrated within a new formalism which also defines a new family of stack-based decoders. These decoders allow s a tradeoff to be made between the advantages of using only one or multiple sta cks. The key point of the new formalism consists in parameterizeing the number of stacks to be used during the decoding process, and providing an efficient method to decide in which stack each partial hypothesis generated is to be insertedd uring the search process. Experimental results are also reported for a search algorithm for phrase-based statistical translation models.