A grammar G is LL(1) if and only if the following conditions hold for two…

A grammar is LL(1) iff, for every pair of distinct alternatives A → α | β, three conditions all hold:

1) FIRST(α) and FIRST(β) share no terminal — otherwise the parser cannot decide between α and β on a common lookahead. This is condition I.

2) At most one of α and β can derive the empty string λ; both cannot, or the parser table entry under a single column would collide. This is condition II.

3) If one alternative is nullable (λ ∈ FIRST(β)), then FIRST(α) ∩ FOLLOW(A) must be empty, so the lookahead that follows A is not also a valid start of the non-empty alternative. This is condition III.

All three conditions are necessary and together sufficient for LL(1), so conditions I, II and III must all hold.