LL1 parsing algorithm for strings generated by a given grammar
Here's a possibly useful quote from Aho, Lam et al (&quot;the Dragon Book&quot;). (Emphasis added.)

A grammar $G$ is $LL(1)$ if and only if whenever $a \to \alpha | \beta$ are two distinct productions of $G$, the following conditions hold:

For no terminal $a$ do both $\alpha$ and $\beta$ derive strings beginning with $a$.

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