# What does ∗⇒mean?

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 $A$.

• I tried to clean up your mathematical notation, but I'm not sure I got it right. If I did it wrong, please tell me what needs to change so that I can fix it, or better still, tell us where you saw the notation so that I can look it up and see how it is written. – MJD Mar 24 '15 at 19:34

## 1 Answer

It's hard to know without seeing the source; mathematical notation is not as standard as you seem to think.

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.