\[ \newcommand{\tr}{\Rightarrow} \newcommand{\trs}{\tr^{\!\ast}} \newcommand{\rlnm}[1]{\mathsf{(#1)}} \newcommand{\rred}[1]{\xrightarrow{#1}} \newcommand{\rreds}[1]{\mathrel{\xrightarrow{#1}\!\!^*}} \newcommand{\cl}{\mathsf{Cl}} \newcommand{\pow}{\mathcal{P}} \newcommand{\matches}{\mathrel{\mathsf{matches}}} \newcommand{\kw}[1]{\mathsf{#1}} \newcommand{\andop}{\mathrel{\&\!\&}} \newcommand{\orop}{\parallel} \newcommand{\ff}{\mathsf{false}} \newcommand{\tt}{\mathsf{true}} \newcommand{\abra}[1]{\langle #1 \rangle} \newcommand{\bnfnt}[1]{\abra{\small \textsf{#1}}} \newcommand{\llbracket}{[\![} \newcommand{\rrbracket}{]\!]} \newcommand{\first}{\mathsf{First}} \newcommand{\nullable}{\mathsf{Nullable}} \newcommand{\follow}{\mathsf{Follow}} \newcommand{\tm}[1]{\mathsf{#1}} \newcommand{\nt}[1]{\mathit{#1}} \newcommand{\Coloneqq}{::=} \newcommand{\abs}[1]{|#1|} \]

We define the parsing table, usually $T$, for a given grammar as a 2d array in which each entry $T[X,a]$ is a set of production rules from the grammar, such that some rule $X \Coloneqq \beta$ is in the set $T[X,a]$ just if, either:

1. $a \in \first(\beta)$
2. or, $\nullable(\beta)$ and $a \in \follow(X)$

A grammar whose parsing table contains at most one rule in each cell is called LL(1).