The algorithms I've seen for building an LL(1) parse table involve calculating first and follow sets such that:

predict(nonterminal, production) == 
     if epsilon in FIRST(production):
         first(production) union follow(nonterminal)

where production is a sequence of symbols which can include nonterminals, terminals, and epsilon.

what's the algorithm for an LL(2) parse table?


1 Answer 1


There is a pretty reasonable discussion in this essay from the SLK parser generator.

Basically, you just need to extend $FIRST$ and $FOLLOW$ to be $FIRST_k$ and $FOLLOW_k$, meaning the first / following $k$ symbols. The basic principle is the same, but when $k > 1$ there is a complication, leading to the distinction between "strong" and regular grammars.

The naming is a bit counterintuitive; the parsing table for a strong grammar can be generated by an easier but less powerful algorithm, so the strong grammars are in a sense weaker; they make a stronger guarantee about predictability.


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