Due to the collapsing of transitive predictions, this step can be
implemented in a very efficient and straightforward manner.
As explained in Section 4.5, one has to
perform a single pass over the current state set, identifying all
nonterminals Z occurring to the right of dots, and add
states corresponding to all productions 
that
are reachable through the left-corner relation .
As indicated in equation (3), contributions to the forward
probabilities of new states have to be summed when several paths lead to
the same state.
However, the summation in equation (3) can be
optimized if
the 
values for all old states with the same nonterminal Z
are summed first, and then multiplied by 
.
These quantities are then summed over all nonterminals Z, and the
result is once multiplied by the rule probability
to give the forward probability for the predicted state.