Let w be a unit and let h be its conditioning history within the n-gram model.
for a given shrink factor γ, the transition corresponding to the n-gram hw is removed from the weighted automaton if: where h is the backoff sequence associated with h. a higher-order n-gram hw is pruned when it does not provide a probability estimate significantly different from the corresponding lower-order n-gram sequence h w. This standard shrinking method needs to be modified to be used in the case of our halfphone-to-unit weighted transducer model with the restriction on the traversal of the backoff transitions described in the previous section.