A few intuitive abbreviations are used from here on to describe
Earley transitions succinctly.
(1) To avoid unwieldy 
notation we adopt the following convention.
The expression
means that x is computed incrementally as a sum of various
y terms,
which are computed in some order and accumulated to finally yield the
value of x.
(2)
Transitions are denoted by 
, with
predecessor states on the left and successor states on the right.
(3)
The forward and inner probabilities of states are notated
in brackets after each state, e.g.,
is shorthand for
,
.