Efficient construction of LALR Parsing Tables

Hello.


I am writing an LALR(1) parser-generator using the "Efficient
Construction of LALR Parsing Table" techniques from the dragon book. I
have a question regarding the parsing actions generated by I from the
kernel alone.




" Reduction by A -> e is called for on input a if and only if there is
a kernel item [B -> g · Cd, b] such that C => An for some n, and a is
in FIRST(ndb). The set of nonterminals A such that C => An can be
precomputed for each nonterminal C."


"We shift on input a if there is a kernel item [B -> g · Cd, b] where
C => ax in a derivation in which the last step does not use an
e-production. The set of such a's can also be precomputed for each C"


(Note. "e" means the empty string and "=>" means a rightmost derives in
zero or more steps,)


I don't know how to precompute the set of nonterminals A and the set of
terminals a. I think that the only way to precompute this sets is
derive the grammar, but this isn't efficient.

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