Prediction is mediated by the left-corner relation. For each X occurring to the right of a dot, we generate states for all Y that are reachable from X by way of the relation. This reachability criterion has to be extended in the presence of null productions. Specifically, if X has a production then is a left corner of X iff all have a non-zero probability of expanding to . The contribution of such a production to the left-corner probability is
The old prediction procedure can now be modified in two steps. First, replace the old relation by the one that takes into account null productions, as sketched above. From the resulting compute the reflexive transitive closure , and use it to generate predictions as before.
Second, when predicting a left corner Y with a production , add states for all dot positions up to the first RHS nonterminal that cannot expand to , say from through . We will call this procedure ``spontaneous dot shifting.'' It accounts precisely for those derivations that expand the RHS prefix without consuming any of the input symbols.
The forward and inner probabilities of the states thus created are those of the first state , multiplied by factors that account for the implied -expansions. This factor is just the product , where j is the dot position.