Closure operation

. If I is a set of items for a grammar G then closure(I) is a set constructed as follows:

- Every item in I is in closure (I)

- If A α .B ß is in closure(I) and B γ is a production then B . γ is in closure(I)

. Intuitively A α .B ß indicates that we might see a string derivable from B ß as input

. If input B γ is a production then we might see a string derivable from γ at this point

As stated earlier, closure operation requires us to find all such alternate ways to expect further input. If I is a set of items for a grammar G then closure( I ) is the set of items constructed from I by the two rules:

1. Initially, every item in I is added to closure (I).

2. If A α .B ß is in closure( I ) and B γ is a production then add the item B . γ to I , if it is not already there. We apply this rule until no more new items can be added to closure( I ).

Intuitively A α .B ß in closure( I ) indicates that, at some point in the parsing process, we think we might next see a substring derivable from B ß as input. If B γ is a production, we also expect we might see a substring derivable from γ at this point. For this reason, we also include B . γ in closure( I ).