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Complete Search Space Exploration for SITG Inside Probability. Proceedings of the Structural, Syntactic and Statistical Pattern Recognition, Joint IAPR International Workshop, SSPR SPR 2010, 2010.Stochastic Inversion Transduction Grammars are a very powerful formalism in Machine Translation that allow to parse a string pair with ecient Dynamic Programming algorithms. The usual parsing algorithms that have been previously dened cannot explore the complete search space. In this work, we propose important modications that consider the whole search space. We formally prove the correctness of the new algorithm. Experimental work shows important improvements in the probabilistic estimation of the models when using the new algorithm.