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.