I have the following grammar I made up:
S -> a a a t | a a a a
I'm trying to prove that it's not LL(3). I found that First(S)={a} and Follow(S)={$} but I can't seem to figure out what I need to do to disprove it being LL(3). It's a small grammar I built for myself to understand how to disprove LL(k). For LL(1) I build a table and in each field I insert the rule base on there First/Follow. But with lookahead 3 how can I do it?
To prove a grammar is (not) LL(3), you need to construct an LL(3) parser for it and show that there is (or is not) a conflict in the resulting table.
To construct the parser tables for LL(3) you need FIRST3 and FOLLOW3, which are analogous to FIRST and FOLLOW, except they are sets of sequences of (up to) 3 tokens, rather than sets of single tokens. So you get FIRST3(S) = { "aaa" } which can select either production for S, giving you a conflict in the table between those productions.
