I am still really new to mathematical notations, and I am still having difficulty understanding most of the languages and notations.
A recent notation I am very confused about is:$\def\starrow{\stackrel\ast\Rightarrow}\starrow$ .
I found that ⇒ means material implication (http://en.wikipedia.org/wiki/List_of_logic_symbols), and * to be (http://en.wikipedia.org/wiki/Kleene_star).
An explanation in laymen's term, or more conceptually based, would be preferred, thanks!
The example I was looking at was:
$$\begin{align}
S2
&\starrow \underbrace{S1S1 \cdots S1}_{\text{$n$ times}} | \{z \}\\
S2 & ⇒ \underbrace{S1S1 \cdots S1}_{\text{$n$ times}} | \{z \} \\
& ∗⇒ w1w2\cdots wn = w
\end{align}$$
Where $S2$ belongs to a grammar in $A^*$ and $S1$ belongs to a grammar in $A$.
Best Answer
It's hard to know without seeing the source; mathematical notation is not as standard as you seem to think.
$\def\starrow{\stackrel\ast\Rightarrow}$ But my guess is that in this case $A\Rightarrow B $ means that $A$ expands in one step to $B$, and $A\starrow B$ means that $A$ expands in to $B$ in zero or more steps.
Put another way, $\starrow$ is the reflexive transitive closure of $\Rightarrow$.
Material implication and the Kleene closure are probably not relevant here.