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 , .